The following parishes records have been searched without finding any STERRYS:

Acrise  (Baptisms, Marriages & Burials 1600-1755)
Addington (Baptisms, Marriages & Burials 1562-1812)
Alkham  (Baptisms, Marriages & Burials 1640-1755)
Allington (Baptisms & Burials 1630-1812, Marriages 1640-1803)
Ash-next-Ridley (Baptisms 1560-1812, Marriages 1562-1812 & Burials 1553-1812)
Badlesmere - St Leonard  (Baptisms, Marriages & Burials 1563-1984)
Barfreyston  (Baptisms, Marriages & Burials 1640-1755)
Benenden (Baptisms, Marriages and Burials Pre 1601)
Bethersden (Baptisms, Marriages and Burials Pre 1601)
Betteshanger  (Baptisms, Marriages & Burials 1640-1755)
Bexley (Baptisms, Marriages & Burials 1566-1812)
Biddenden (Baptisms, Marriages and Burials Pre 1601)
Birling (Baptisms, Marriages & Burials 1558-1812)
Blackheath - Morden College Chapel (Baptisms, Marriages & Burials 1702-1911)
Boughton under Blean (Baptisms 1558-1624, 1784-1812; Marriages 1558-1626, 1784-1812 and Burials 1558-1625, 1784-1812)
Brasted - St Martins (Baptisms 1813-1867, Marriages 1754-1867, Burials 1813-1867)
Brenchley - All Saints (Baptisms 1566-1837, Marriages 1560-1837, Burials 1560-1837)
Bromley - Holy Trinity (Burials 1844-1883)
Buckland (Baptisms, Marriages & Burials 1640-1755)
Burham (Baptisms, Marriages & Burials 1626-1812)
Canterbury - Marriage Licences 1701-1750, 1811-1849; Marriage & General Licence Registers 1850-1916)
Canterbury Cathedral (Baptisms, Marriages & Burials 1564-1878)
Canterbury - All Saints (Marriages 1754-1828, Banns 1754-1828)
Canterbury - St Dunstan (Baptisms 1743-1857, Burials 1743-1969)
Canterbury St Peter (Baptisms, Marriages & Burials 1560-1800)
Canterbury-Hales Place (Catholic) (Baptisms, Marriages & Burials 1793-1803)
Capel-le-Ferne (Baptisms, Marriages & Burials 1640-1755)
Chalk (Baptisms, Marriages & Burials 1661-1812)
Charton (Baptisms, Marriages & Burials 1661-1755)
Charlton in Dover (Marriages 1565-1812 - Phillimores)
Chatham, St Mary (Baptisms 1567-1675, Marriages 1567-1675 & Burials 1567-1675)
Chelsfield (Baptisms, Marriages & Burials 1558-1812)
Chevening (Baptisms 1561-1812, Marriages & Burials 1568-1812)
Chislehurst, St Nicholas (Baptisms 1559-1880, Marriages 1558-1754 & Burials 1559-1899)
Chislet (Baptisms, Marriages & Burials 1538-1707)
Cliffe, St Helen (Burials 1558-1985)
Cobham St Mary Magdalene's (Baptisms 1655-1812, Marriages 1676-1812 & Burials 1668-1812)
Coldred (Baptisms, Marriages & Burials 1600-1755)
Cooling (Baptisms 1707-1812, Marriages 1712-1812 & Burials 1708-1812)
Cranbrook (Baptisms, Marriages and Burials Pre 1601)
Cray, North - St James (Baptisms, Marriages & Burials 1538-1812)
Cray, St Mary - St Mary (Baptisms, Marriages & Burials 1579-1812)
Crayford - St Paulinus  (Baptisms, Marriages & Burials 1558-1812)
Cudham - St Peter & St Paul  (Baptisms, Marriages & Burials 1653-1812)
Cuxton - St Michael  (Baptisms, Marriages & Burials 1560-1812)
Darenth  (Baptisms, Marriages & Burials 1678-1812; Marriages 1813-1837; Burials 1813-1884)
Dartford - Holy Trinity (Baptisms, Marriages & Burials 1561-1812)
Deal St Leonard (Baptisms, Marriages & Burials 1559-1837)
Deal - St George (Baptisms 1781-1807, 1809-1842, 1852-1950; Marriages 1717-1752, 1852-1956; Burials 1737-1717, 1809-1842, 1852-1911)
Deal-St Thomas & Walmer Convent of the Visitation (Catholic) (Baptisms 1850-1928, Marriages 1856-1920 & Burials 1856-1977)
Denton (Baptisms, Marriages & Burials 1600-1755)
Deptford - St Paul (Burials 1788-1812)
Ditton - St Peter (Baptisms, Marriages & Burials 1663-1812)
Dover - St James the Apostle (Baptisms, Marriages & Burials 1640-1755)
Dover-St John Mariner (Baptisms 1849-1906)
Dover - St Mary (Baptisms, Marriages & Burials 1640-1755)
East Greenwich - Christchurch (Baptisms 1868-1912)
Eastry (Baptisms, Marriages & Burials 1640-1755)
Elham (Baptisms, Marriages & Burials 1585-1755)
Eynsford - St Martin (Baptisms, Marriages & Burials 1538-1837)
Eythorne (Baptisms, Marriages & Burials 1640-1755)
Ewell (Baptisms, Marriages & Burials 1640-1755)
Eynsford Baptist (Baptisms & Burials 1813-1837)
Eythorne East-Baptist Church (Births 1723-1837)
Farnborough, St Giles the Abbot (Baptisms, Marriages & Burials 1538-1652)
Farningham - St Peter & St Paul (Baptisms, Marriages & Burials 1589-1812)
Fawkham - Chantry of St Mary (Baptisms, Marriages & Burials 1568-1812)
Fleet, South - St Nicholas  (Baptisms, Marriages & Burials 1558-1812)
Foots Cray (Baptisms & Burials 1559-1812, Marriages 1567-1812)
Frindsbury - All Saints (Baptisms, Marriages & Burials 1669-1812)
Frittenden (Baptisms, Marriages and Burials Pre 1601)
Goudhurst (Baptisms, Marriages and Burials Pre 1601)
Gravesend - St George (Baptisms, Marriages & Burials 1547-1812)
Guston (Baptisms, Marriages & Burials 1667-1755)
Halling - St George (Baptisms, Marriages & Burials 1705-1812)
Halstead (Baptisms, Marriages & Burials 1561-1812; Marriages 1561-1836-Phillimores)
Halstow, High - St Margaret (Baptisms, Marriages & Burials 1653-1812)
Ham (Baptisms, Marriages & Burials 1640-1755)
Hartley - All Saints (Baptisms, Marriages & Burials 1712-1812)
Hawkinge (Baptisms, Marriages & Burials 1662-1755)
Hayes - St Mary (Baptisms, Marriages & Burials 1539-1812)
Headcorn (Baptisms, Marriages and Burials Pre 1601)
Higham - St Mary (Baptisms, Marriages & Burials 1653-1812)
High Halden (Baptisms, Marriages and Burials Pre 1601)
Hoo - St Mary (Baptisms & Marriages 1695-1812; Burials 1695-1977)
Hoo - St Weburgh (Baptisms, Marriages & Burials 1695-1985)
Horton Kirkby - St Mary (Baptisms, Marriages & Burials 1678-1812)
Hougham (Baptisms, Marriages & Burials 1659-1755)
Hunton - St Mary (Baptisms, Marriages & Burials 1585-1812)
Ifield - St Margaret (Baptisms, Marriages & Burials 1751-1812)
Kemsing - St Mary (Baptisms, Marriages & Burials 1561-1812)
Keston (Baptisms, Marriages & Burials 1540-1812)
Kingsdown (Baptisms, Marriages & Burials 1725-1812)
Knockolt - St Catherine (Baptisms, Marriages & Burials 1548-1812)
Lamberhurst (Marriages 1564-1837-Phillimores)
Langdon, East (Baptisms 1561-1889, Marriages 1561-1837 & Burials 1561-1889)
Langdon, West (Baptisms, Marriages & Burials 1661-1755)
Leaveland (Baptisms 1558-1984, Marriages 1554-1976 & Burials 1553-1902)
Lee, St Margaret (Baptisms, Marriages & Burials 1579-1754)
Leigh - St Mary (Baptisms, Marriages & Burials 1592-1812)
Leybourne - Sts Peter & Paul (Baptisms, Marriages & Burials 1560-1812)
Longfield - St Mary (Baptisms, Marriages & Burials 1558-1812)
Luddesdown - Sts Peter & Paul (Baptisms, Marriages & Burials 1681-1812)
Lullingstone - St Botolph (Baptisms, Marriages & Burials 1578-1812)
Lydden (Baptisms, Marriages & Burials 1637-1755)
Marden (Baptisms, Marriages and Burials Pre 1601)
Meophan - St John the Baptist (Baptisms, Marriages & Burials 1561-1812)
Mereworth - St Lawrence (Baptisms, Marriages & Burials 1559-1812)
Milton-next-Sittingbourne Paradise (Non-Conformist) Chapel (Baptisms 1807-1836)
Milton-next-Sittingbourne Methodist Chapel (Baptisms 1798-1837)
Minster in Thanet - St Mary (Baptisms 1557-1962, Marriages 1557-1922, Burials 1557-1944)
Mongeham  (Baptisms, Marriages & Burials 1661-1755)
Newenden (Baptisms, Marriages & Burials 1559-1812)
Newington (Marriages 1559-1837 - Phillimores)
Northbourne  (Baptisms, Marriages & Burials 1640-1755)
Northfleet (Baptisms, Marriages & Burials 1538-1812)
Nursted - St Mildred (Baptisms, Marriages & Burials 1561-1812)
Offham - St Mildred  (Baptisms, Marriages & Burials 1538-1812)
Orpington - All Saints  (Baptisms, Marriages & Burials 1755-1812)
Otford - St Bartholomew  (Baptisms, Marriages & Burials 1630-1812)
Paddlesworth  (Baptisms, Marriages & Burials 1662-1755)
Peckham East - St Michael  (Baptisms, Marriages & Burials 1558-1812)
Peckham West - St Dunstan  (Baptisms, Marriages & Burials 1561-1812)
Pembury (Marriages 1560-1812)
Penshurst - St John  (Baptisms, Marriages & Burials 1538-1812)
Plaxtol  (Baptisms, Marriages & Burials 1648-1812)
Ramsgate, St Marys (Baptisms 1886-1932)
Ridley - St Peter (Baptisms, Marriages & Burials 1626-1812)
Ringwould  (Baptisms, Marriages & Burials 1640-1755)
Ripple  (Baptisms, Marriages & Burials 1640-1755)
River, St Peter & St Paul (Baptisms 1620-1840, Marriages 1661-1837 & Burials 1664-1839)
Rochester Marriage Licences (1637-1639, 1715-1716, 1731-1767, 1770-1772, 1774-1775, 1777-1840)
Rolvenden (Baptisms Pre 1601, Marriages 1558-1837 and Burials Pre 1601)
Ryarsh - St Martin  (Baptisms, Marriages & Burials 1560-1812)
Saint Lawrence in Thanet (Baptisms 1560-1914, Marriages 1559-1906, Burials 1559-1983)
Saint Margaret at Cliffe  (Baptisms, Marriages & Burials 1640-1755)
Saint Peter in Thanet (Broadstairs) (Baptisms 1582-1852, Marriages 1582-1883, Burials 1582-1875)
Sandhurst (Baptisms, Marriages and Burials Pre 1601)
Seal - St Peter  (Baptisms, Marriages & Burials 1561-1812)
Selling, St Mary the Virgin (Baptisms 1558-1979 , Marriages & Burials 1560-1979)
Sheldwich - St James (Baptisms, Marriages & Burials 1560-1984)
Shepherdswell  (Baptisms, Marriages & Burials 1600-1755)
Shipbourne - St Giles  (Baptisms, Marriages & Burials 1658-1812)
Sholden  (Baptisms, Marriages & Burials 1640-1755)
Shoreham - Sts Peter & Paul  (Baptisms, Marriages & Burials 1558-1812)
Shorne - Sts Peter & Paul  (Baptisms, Marriages & Burials 1538-1812)
Smarden (Baptisms, Marriages and Burials Pre 1601)
Snodland - All Saints  (Baptisms, Marriages & Burials 1559-1812)
Stansted - St Mary  (Baptisms, Marriages & Burials 1564-1812)
Staplehurst (Baptisms, Marriages and Burials Pre 1601; Marriages 1538-1812-Phillimores)
Stone-next-Dartford - St Mary  (Baptisms, Marriages & Burials 1718-1812)
Sundridge  (Baptisms, Marriages & Burials 1562-1812)
Sutton  (Baptisms, Marriages & Burials 1640-1755)
Sutton at Hone - St John the Baptist  (Baptisms 1607-1868;   Marriages 1607-1837;  Burials 1607-1812)
Swanley - St Paul (Burials 1862-1982)
Swanscombe - Sts Peter & Paul  (Baptisms, Marriages & Burials 1559-1812)
Swingfield (Baptisms, Marriages & Burials 1661-1755)
Tenterden (Baptisms, Marriages and Burials Pre 1601)
Teston - St Peter & St Paul  (Baptisms, Marriages & Burials 1538-1812)
Throwley, St Michael & All Angels (Baptisms 1557-1960, Marriages 1557-1980 & Burials 1557-1980)
Tilmanstone - St Andrews (Baptisms, Marriages & Burials 1558-1900)
Trotterscliffe - St Peter & Paul  (Baptisms, Marriages & Burials 1540-1812)
Waldershare (Baptisms, Marriages & Burials 1640-1755)
Walmer, St Mary (Baptisms 1560-1945, Marriages 1561-1921 & Burials 1560-1988)
Wateringbury - St John the Baptist  (Baptisms, Marriages & Burials 1705-1812)
Westcliffe (Baptisms, Marriages & Burials 1640-1755)
Westerham (Marriages 1559-1837-Phillimores)
West Farleigh (Marriages 1558-1812 - Phillimores)
Wichling (Marriages 1577-1837-Phillimores)
Wickham East - St Michael  (Baptisms, Marriages & Burials 1715-1812)
Willesborough (Marriages 1538-1837-Phillimores)
Wilmington - St Michael  (Baptisms, Marriages & Burials 1683-1812)
Wingham Congregational Chapel (Baptisms 1819-1837)
Wittersham (Baptisms, Marriages and Burials Pre 1601)
Woodchurch (Baptisms, Marriages and Burials Pre 1601)
Woolwich (St Mary Magdalene) (Baptisms, Marriages and Burials 1813-1837 - Modern Transcript & Index)
Wooton (Baptisms, Marriages & Burials 1640-1755)
Worth (Baptisms, Marriages & Burials 1663-1755)
Wye (Baptisms 1538-1812, Marriages 1545-1805 & Burials 1538-1812)
Yalding - St Peter & St Paul (Baptisms, Marriages & Burials 1559-1812)

The following parishes have been searched and have located STERRYS or similar:

Aylesford St Peter's
Baptisms 1653-1812
Nil

Aylesford St Peter's
Marriages 1653-1812
1672/3 Feb 4 Joshua Austen of Loose Joyner & Ann Stere of Brenchley by Licence Rochester

Aylesford St Peter's
Burials 1653-1812
Nil

Canterbury
Marriage

There is an IGI marriage entry:
1718 May 25 Elizabeth Starey & John Atwood, Canterbury

Charlton
Baptisms 1562-1840
Nil

Charlton
Marriages 1562-1829
1828 Apr 8 James Sterry of this Parish, Bachelor and Elizabeth Yeates of the same, Spinster, were married in this Church by Banns Wit: Charles Peck, Elizabeth Holden

Charlton
Burials 1562-1850
Nil

Cowden
Baptisms

There are IGI baptism entries:
1688 Jun 9 Anne Starey d. John Starey, Cowden
1702 Jul 4 Robert Starey d. Anne Starey, Cowden

Cray, St Pauls - St Paulinus
Baptisms 1579-1812
1600 Jun 11 Mary Stere daughter of John Stere
1607 Oct 2 Margaret Stere and Sarah Stere daughters of John Stere

Cray, St Pauls - St Paulinus
Marriages 1579-1812
Nil

Cray, St Pauls - St Paulinus
Burials 1579-1812
Nil

Deptford St Paul
Baptisms 1838-1859 (PR)
Nil

There is an IGI baptism entry:
1869 Aug 29 Edward Starey s. Michael Starey & Jane

Walter Smith in The Sterry Family notes the administration of the estate of Anthony Sterry in Oct 1681 mentions that Anthony was of Deptford and he had two brothers Robert & Thomas.

Faversham

Walter Smith in The Sterry Family:Miscellaneous says there were Sterrys in Faversham. In particular, a Thomas Sterry, his wife Anne French, his son Samuel born before 1631 and his sons Thomas, Charles & Benjamin born after 1631.

Hawkhurst
Baptisms Pre 1601
1574/75 Jan 16 Richard son of Arthur Sterrey
1576 Sep 2 Nichol daughter Arthur Sterrey
1578 Apr 8 Fortescue son of Arthur Sterrey
1579/80 Jan 24 Anne daughter Arthur Sterrey
1581/82 Feb 25 Arthur son of Arthur Sterrey

Hawkhurst
Marriages Pre 1601
1574 May 13 Arthur Stirrey & Agnes Greenell

Hawkhurst
Burials Pre 1601
1581/2 Mar 9 Arthur Sterrye s of Arthur
1587 Jun 26 Arthur Sterrye
1589 Sep 22 Agnes Sterrie

Ightham - St Peter
Baptisms 1559-1812
Nil

Ightham - St Peter
Marriages 1559-1812
1587 Jul 16 Richard Lillie & Elizabeth Sterrie

Ightham - St Peter
Burials 1559-1812
Nil

Kennington
Baptisms

There are IGI baptism entries:
1831 Dec 9 Elizabeth Jane Starie d. of John Joseph Starie & Elizabeth, Kennington, Saint Mark
1837 Jul 12 Jane Starie d. William Starie & Jane, Kennington, Saint Mark
1842 Jul 20 Fanny Starie d. William Starie & Jane, Kennington, Saint Mary Magdalene
1849 May 27 Major Major Starey s. Major Major Starey & Sarah, Kennington, Saint Mark
1852 Sep 17 Sarah Elizabeth Starey d. Major Major Starey & Sarah Maria, Kennington, Saint Mark
1865 Aug 6 Olive Ellen Sterry d. Robert Wright Sterry & Olive, Kennington, Saint Mark

Lyminge 
Baptisms 1660-1755
There is a baptism in an index for this parish:
1699 STERRIE An Father: Jas, Mother: An

Lyminge 
Marriages 1660-1755
Nil

Lyminge 
Burials 1660-1755
Nil

Malling, East - St James
Baptisms 1570-1812
Nil

Malling, East - St James
Marriages 1570-1812
Nil

Malling, East - St James
Burials 1570-1812
1621 Jan 21 Charles Sterry

Milton (Sittingbourne)
Marriage

There is an IGI marriage:
1673 Jun 9 Stephen Stary and Elizabeth Woods, Milton Next Sittingbourne

Milton-next-Gravesend
Baptisms 1559-1812
Nil

Milton-next-Gravesend
Marriages 1559-1812
Nil

Milton-next-Gravesend
Burials 1559-1812
1672 Aug 24 William Starre a seaman

Shoreham

There is a baptism in the LDS Vital Records British Isles:
**STERRY, Eliza Round    Christening
Sex:    Female
Christening Date:    29 Jun 1834    Recorded in:     Shoreham, Kent, England
Father:    William Bristow STERRY
Mother:    Betsy Louisa
Source:    FHL Number 1469564    Dates:     1813-1904

Wrotham - St George 
Baptisms 1558-1812
1577 Dec 12 Abner son of William & Magdalin Stere
1579 Jul 12 Mary daughter of William Steere
1580/81 Mar 21 Anna daughter William Stere
1582 Dec 2 William son William Stere
1586 Oct 30 Benoaie(?) son William Steere
1594 Sep 15 Thomas son William Steere
1788 Aug 10 Sarah daughter Thos Steer & Mary

Wrotham - St George 
Marriages 1558-1812
1593 Aug 15 William Steere & Elenor Greene

Wrotham - St George 
Burials 1558-1812
1584 Aug 10 Magdalene ye wife of William Stere
1589 May 11 Jane ye wife of William Stere

There were no Sterrys found in Canterbury Marriage Licences 1751-1837

Legend:

** = Lowestoft, Suffolk, UK line