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 John O'Malley B ???? in Galway (west) with a father forenamed Mat--, I found 5 B rcds: 1841, 1875, 2-1895, and 1900.
For Bridget Connelly B 1885 +/- 4 yrs with a father named Pat(rick), I found 5 B rcds: 1882, 1883, 1884, 1886, and 1889.
For Mathias O'Malley, I found neither B nor M rcds for anydate, anywhere in Galway east or west.
Some of the above MAY be for your ancestors - there are no guarantees. Will leave it to you to experiment with date ranges, names, etc., to eliminate false positives. A view of the detailed rcd(s) should show which, if any, is right.
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.