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 Pat(rick) Gavin M 1870 +/- 4 yrs in Co. Galway, I found 5 rcds in 1856, 1881, 1888, 1888, and 1891 Moycullen.
For Bri(dget) Flannagan M ditto, I foundrcds 3-1859, 1866, 2-1867, 1874, 2-1876, 1886, and 3-1891. The only POTENTIAL match was for 1891. However, there was NO match at the parish level. They may have married elsewhere, or the rcd didn't survive.
For Pat(rick) Gavin B 1840-1850 in Co. Galway with the father's forename unknown, I found 4 rcds: 1840, 1842, 1845, and 1849. Father's forenames were Richard, Mat(thew), Stephen, and Thomas respectively. The 1845 rcd is in Kilcummin-Oughterard RC parish. This stands a good chance of being for your ancestor.
For Bri(dget) Flannagan B ditto, I found 9 rcds: 3-1840, 1842, 1844, 2-1846, and 2-1848. None of these were in Oughterard parish. The rcd may not have survived.
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.