I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For John McMahon B 1846 (exact), somewhere in Ireland, with a father forenamed John, I found 12 rcds - too many to summarize here.
For Mary McGinty M ditto, I found 4 rcds: 1838 Longford, 1844 Derry, 1846 Mayo, and 1846 Westmeath.
For John McMahon M 1842 +/- 4 yrs, in the same parishes as found for Mary, I found 14 rcds. Only 1 in 1846 Mayo has the POTENTIAL for being a match. Searching at the parish level, there is NO match. Either the rcd(s) didn't survive, or haven't been transcribed yet.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.