Why did you mention perhaps Portaferry ? Portaferry is in the parish of Ballytrustan and Ballyphillip
1823-1837 The Tithe applotment books exist in the Public Record Office Belfast, an index exists
http://www.irishgenealogyhub.com/down/tithe-applotment-books/ballyphilip-parish.php#.WWE4ysaZP9M which has 2 entries, the first without a first name
Conner, Townland: Ballyphilip Year: 1827-Ballyphilip-Down-
Conner, Widow Townland: Ballyphilip Year: 1827-Ballyphilip-Down-
1863 Griffiths Valuation has
Connor Patrick Back Lane,Portaferry Ballyphilip Down
Connery James Craigaroddan Ballyphilip Down
Ros Davies Co Down website
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/ has many Connor and a few Conner but I dint find a mention of James elias
Miss Eliza CONNER . Ballyphilip regd. Portaferry; wife of George McVay; mother of male child b. 1865 CR
John CONNOR . Ballyphilip brother of George Connor who died 13 Apr 1848 aged 25; grandson of Eliza Kelly (d. 16 Jun 1843) & buried Templecranny graveyard, Portaferry MIs
Patrick CONNOR . Ballyphilip from Portaferry; an able seaman aged 24 ; served on Lock Ryan of Glasgow then on board British cruiser 'Nelson' which sailed to Port Chalmers, Otago, New Zealand in 1881 SSSCP p59
ancestryireland doesn’t have, familysearch.org doesn’t have
church records download
https://www.nidirect.gov.uk/sites/default/files/publications/Guide_to_church_records.pdfBALLYPHILIP, CO. DOWN
C.I. Ballyphilip (Down diocese)
Baptisms, 1745-1871; marriages, 1746-1844; marriage notices, 1851-65; burials, 1745-1883; poor lists, 1808-13.
Baptisms, 1872-; marriages, 1845-; vestry minutes, 1751-; register of vestrymen, 1870-; preachers’ books, 1886-.
M. Portaferry (Newtownards Circuit)
Baptisms, 1870-c.1880; circuit schedule book, 1870- 78.
P. Portaferry
Baptisms, 1699-1786 and 1822-1953; marriages, 1750-84 and 1822-1936; marriage notice books, 1879- 1906; burials, 1836-1989; list of members who emigrated, 1852-72; communicants’ roll, 1870; receipts and accounts, 1841-1916; title deeds and legal papers, 1778-1893; testamentary papers, 1812- 69.
Marriages, 1785-1822; communicants and poor lists, 1803-34; minutes, 1822-.
87
R.C. Ballyphilip and Portaferry (Down and Connor diocese) [Contains most of the civil parishes of Ardquin, Ballyphilip and Ballytrustan]
Baptisms, marriages and some funerals, 1843-81.
goodluck you will need it