to have some sort of a start, I looked at the locations listed in the incomplete 1823-1837 Tithes Applotment Books based upon the index work of the Irish Genealogy Hub’s listing for each civil parish in Northern Ireland, which are quicker to lookup if you know the parish! The relevant original books are in the Public Record Office of Northern Ireland (PRONI) Belfast
the actual record is a one line no help in genealogy other than identifying possible locations for namesname in a place
I found 5 civil parishes out of 79 parishe in Co Antrim including spelling variants
Ballintine, J. Townland: Legavar Year: 1824 Ballintoy Antrim
Ballintine, John Townland: Maghernahar Year: 1824 Ballintoy Antrim
Ballintine, Danl. Townland: Prolisk Year: 1824 Ballintoy Antrim
Ballintine, John Townland: Prolisk Year: 1824 Ballintoy Antrim
Ballentine, Jas. Townland: Ballykeel Year: 1825 Ballyclug Antrim
Ballentine, John Townland: Ballykeel Year: 1825 Ballyclug Antrim
Ballentine, Robt. Townland: Crebilly Year: 1825 Ballyclug Antrim
Ballentine, John Townland: Skelgan Year: 1833 Ballynure Antrim
Ballantine, John Townland: Skilganaban Year: 1834 Ballynure Antrim
Ballentine, Wm. Townland: Loughduff Year: 1834 Carncastle Antrim
Ballentin, William Townland: Ballyedward Year: 1834 Kilwaughter Antrim
Ballentine, Thos. Townland: Ballyhampton Year: 1834 Kilwaughter Antrim
Ballentin, William Townland: Drumadonagh Year: 1834Kilwaughter Antrim
Ballentine, Jno. Townland: Headwood Year: 1834 Kilwaughter Antrim
Ballentine, John Townland: Hightown Year: 1834 Kilwaughter Antrim
Ballentine, John Townland: Lowe Town or Bog Town Year: 1834 Kilwaughter Antrim
Ballentine, William Townland: Old Freehold Year: 1834 Kilwaughter Antrim
you could compare ti Griffiths valuation to widen or reduce the possibilities
eg ballintoy, ballnure disappears and Drummaul and Grange of Ballyscullion and grange of Doagh creep in, that’s chacking with just one spelling ie .
you have the spelling with a y. I found none in these two records
Patterson in Tithes process just one match Carncastle the list wasBallinderry Ballymoney Ballyscullion Billy Blaris Carncastle Carnmoney,Carrickfergus Connor Derryaghy Derrykeighan Donegore Drumbeg Dunaghy Dunluce Finvoy Glenavy Killagan Killead Killraghts Loughguile Magheragall Portglenone Rasharkin Skerry Tickmacrevan Tullyrusk the Carncastle is
Patterson, David Townland: Ballygally Year: 1834 Carncastle Carncastle Antrim
plus another spelling
Pattison, Thomas-Townland: Tonagh Year: 1834-Blaris-Antrim
Pattison, Henry-Townland: Burnquarter Year: 1825-Ballymoney-Antrim
Pattison, Henry-Townland: Culdoo Year: 1825-Ballymoney-Antrim
Pattison, Leslie-Townland: Culdoo Year: 1825-Ballymoney-Antrim
Pattison, Margt.-Townland: Anthony Thomas Bogs Year: 1825-Ballymoney-Antrim
Pattison, Robert-Townland: Drumkendult No. 2 Year: 1825-Ballymoney-Antrim
doing ths same with Patterson spelling just in Griffiths produces a big list
of additions Ahoghill Antrim Ardclinis BallinderryBallymoneyBallynure
Ballyrashane Billy Blaris CamlinCarncastleCarnmoneyCarrickfergus
ConnorCraigsDerryaghyDrumbegDrummaulFinvoyGlenavyGlynn
Grange of BallyscullionGrange of MuckamoreGrange of Nilteen
KillaganKilleadKilraghtsKilrootKirkinriolaLarneMagheragallSkerry
TemplecorranTemplepatrickTickmacrevanTullyrusk
Carncastle and adjoins Kilwaughter parish gives this list so that would be my best guess from using records.
the most likely connections including in Carncastle are
Ballentine, Wm. Townland: Loughduff Year: 1834
Patterson, David Townland: Ballygally Year: 1834
Patterson, Widow Townland: Ballygally Year: 1834
Patterson, Wm. Townland: Ballywillen Year: 1834
or in Kilwaughter whicch has no pattersons
Ballentin, William Townland: Ballyedward Year: 1834
Ballentin, William Townland: Drumadonagh Year: 1834
Ballentine, Jno. Townland: Headwood Year: 1834
Ballentine, John Townland: Hightown Year: 1834
Ballentine, John Townland: Lowe Town or Bog Town Year: 1834
Ballentine, Thos. Townland: Ballyhampton Year: 1834
Ballentine, William Townland: Old Freehold Year: 1834
church records see
https://www.nidirect.gov.uk/sites/default/files/publications/PRONI-Guide-to-Church-Records.pdfCarncastle presbt’ records start 1832
Kilwaughterdestroyed in Dublin starts 1883 however Rc records
Good luck you will need loads of it. without more information