I have a great-great grandfather named John McMahon. I believe that he was born in Ireland about 1830 and he subsequently married Jane Coyle. My John had a son Thomas McMahon who married Agnes McCann in Kilmarnock, Scotland on 1 Jan 1866. This family is Catholic. Could he be the one that you are looking for?
I am looking for information about my ggg grandfather, John McMahon. His wife was Jane Nelson or Neilson. Their son, Francis McMahon, was born around 1855 and I bought a copy of a birth certificate but the mother's name was Jane COYLE. Maybe this is your family? I'll try to post a copy on here once I get it scanned.
(Kilmarnock Male Birth, Francis McMahon, 17 July 1855, Father John McMahon, Coal Miner, 35 years, County Monaghan Ireland, Mother Jane McMahon, Maiden Name Coyle, 39 years, County Down, Ireland, married 1844 Kilmarnock, her 6th child, 2 boys living, 1 girl living, 2 boys dead)I'm a Glasgow McMahon and I've traced them back to 1851 here but I don't know where in Ireland they're from. The 1861 census names a daughter, Rosina, born Ireland in 1856 and I'm hoping to get lucky with her.