I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
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 Molloy B 1860 +/- 1 yr somewhere in Ireland with the father forenamed Pat(rick), I found 5 rcds: 1859 Galway, 1860 Down, 2-1861 Mayo, and 1861 Dublin.
For Marg(aret) Flynn B 1862 ditto with a father forenamed Edward, I found 1 rcd in 1863 Westmeath.
For Agnes Flynn B ???? in Co. Westmeath with a father forenamed Edward, I found 0 rcds. This casts doubt on the rcd for Margaret.
Since you have the marriage cert, you likely have the mother's forenames at least. These can help pick the correct, if any, rcds.
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.