Glenys,
The Ulster Historical Foundation has a list of all known graveyards in Ulster. You can search their database free, by townland or parish, and identify those that might help you. Search “Graveyards in Ulster.” 4 are shown for Billy parish – Billy CI, Dunseverick CI, Mosside Presbyterian & Toberdoney Presbyterian.
https://www.ancestryireland.com
The Causeway Coast & Glens Branch of the North of Ireland FHS have transcribed the legible stones in quite a few local graveyards, and the transcriptions can be found on their website. You need to join to access the records.
http://colerainefhs.org.uk
St Patrick’s in Coleraine has this gravestone:
In memory of / James McNaghten Esq, late of Coleraine/ eho departed this life 3rd Dec 1828 / aged 59 years / also / Annie McNaghten his wife / died 26th Jan 1830 / aged 68 years / BARTHOLOMEW McNaghten / of Ballyboggey / son-in-law of th above / who died January 1st 1832 / in the 46th year of his age / also of Catherine / wife of Bartholmew / died at Portstewart 26th March 1867
Is that your family? (A later generation or so obviously, but Bartholomew is a fairly unusual name and perhaps there is a connection?)
I know you visited PRONI so you may have seen these already:
D2977/3A/3/1/75 26 Oct 1736
Copy conveyance from the Rt. Hon. Alexander, Earl of Antrim, to Bartholomew McNaghten Esq., of Benvarden, Co. Antrim, of the two quarters of Ballytaggart, quarter of Carnageeragh, quarter of Toberbilly, quarter of Killymagighy, quarter of Ballylosh, quarter of Drumnabrasly, quarter of Legacurry, half quarter of Feltin [?], quarter of Altarichard, quarter of Knockavrinnan, quarterland of Tullycapple and the quarterland of Ballybogy in consideration of the sum of £1100 sterling. Yearly rent £54.5s.0d. sterling.
D2977/3A/3/1/76 23 Nov 1736
Rt. Hon. Alexander, Earl of Antrim to Bartholomew McNaghten, Benvardin, Co. Antrim. Copy counterpart fee farm deed forever of 2 quarters of Knockanboy and 2 quarters of Conogher, Co. Antrim. Consideration £400. Rent £30. Receiver's Fees 6d per pound. Suit and Service at Manor Courts and Mills. Distrain and Distress.
T1638/30/1 23 Nov 1736
Earl of Antrim to Bartholomew McNaghten, Benvarden, Co. Antrim.
Lease; term forever; yearly rent of £30. Consideration £400.
Two quarterlands of Knockanboy and two quarterlands of Conogher, Co. Antrim.
D282/20 30 July 1762
Mortgage. Bartholomew McNaghten, Carnglass, Co. Antrim and Sarah Steele, Dublin. Consideration £300. Lands at Carnaglass Beg, Lisnagot [Lisnagat] and two quarters of land in Ballywatt, all in the barony of Dunluce, Co. Antrim
D971/42/B/9 17 Dec 1782
Lease for three lives or 11 years, Bartholomew McNaghten of Coleraine, esq., to James Young of East Ballywatt, farmer: property in East Ballywatt, parish of Ballyrashane.
The above 3 lives lease is probably worth looking at as it may name some relatives (ie the other 2 lives) and give their ages.
A colleague has suggested that the McNaghten family originally lived in Benvarden townland which is in Dunluce parish, so there might be graves around there. I think the first McNaghten to settle in Ireland was a cousin of the 1stEarl of Antrim and managed part of the Antrim estate. The McNaghtens originated in Scotland and presumably arrived in the late 1500s/early 1600s, along with the McDonnells.
A genealogist from that area is Dorothy Arthur. She has published a number of books on graveyards in North Antrim, available on Amazon and other similar sources. She has considerable knowledge of the local families and might be able to assist you in your research.
https://www.facebook.com/dorothyaarthur/