Is John your direct ancestor ?
I think the initial search should be for him and his immediate family...
you mentioned Peter Quinn and Margaret Trainor - and there are some births listed to them between 1870 and 1878 in the extracted collection on FamilySearch, but no sign of a John ....
Patrick Quin, 04 Aug 1870, Monaghan
Bernard Quinn, 19 Mar 1872, Kilmore, Monaghan
Margaret Quinn, 17 Mar 1878, Corcaphan, Monaghan
see :
Quinn / Trainor births The extracted births are not complete, so there could be other births to this Peter and Margaret
Shane