You are right to be cautious. There was a civil parish named Ballymoney in County Cork, which could have given rise to confusion when the owner of the tree you have found was doing their research.
Certainly, there was a John Connolly at Castle Street, Townparks, Ballymoney, County Antrim on the 19th December 1832, according to valuation records. This may be at least a starting point for checking further, even if not 'your' John.