Your info is very sketchy. No DOBs for either the parents or children. Will do what I can.
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 parish, 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 Bri(dget) Duddy M ???? in Co. Mayo, I found 6 rcds: 1857, 1862, 2-1896, and 2-1897. The last ones may be civil duplicates of church rcds of the event.
For Pat(rick) Flannigan M ditto, I found 2 rcds in 1897, Addergoole RC parish and Westport district. Neither of these matched the parish/districts for Bridget. It appears the M event wasn't rcd'd in Ireland.
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.