The Will of Thomas Mayne late of Ballyboley County Antrim Farmer deceased who died 18 March 1880 at same place was proved at Belfast by the oaths of John Mayne and James Mayne both of Ballyboley Farmers the Executors. Will dated 25 Dec.1885 mentions daughter Eliza Jane McCookin and sons Robert, John & James.
Thomas Mayne was 87 when he died according to death registration-
LINKLetters of Administration of the personal estate of John Mayne late of Ballyboley County Antrim Farmer who died 4 July 1886 at same place were granted at Belfast to James Mayne of Ballyboley Farmer a Brother.John Mayne was 63 according to death registration-
LINKSince John seems to have been born around 1823 there will be no birth certificate and you'll have to see if a record of his baptism survives (not all early church records do survive and of those that do not all, especially Presbyterian ones, are online).
A John Mayne of Ballyboley died 1909 age 76- so, born c1833-
LINKProbate of the Will of James Mayne late of Ballyboley County Antrim Farmer who died 13 March 1909 granted at Belfast to Thomas Mayne Solicitor's Assistant and John Mayne Farmer. Will dated 10 Dec.1903 mentions sons (John, Thomas, Robert, Andrew, William James, Samuel) & daughter (Lizzie).
www.census.nationalarchives.ie/pages/1901/Antrim/Ballycor/Ballyboley/990738PRONI have microfilmed the registers for 1st Ballyeaston Presbyterian Church-
Baptisms, 1814-1924; marriages, 1813-90; marriage Notices, 1933-2002; indexes to baptisms, 1814-1924; census, 1813.