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 Martin O'Malley B 1848 +/- 4 yrs in Co. Galway with the father's forename unknown, I found 1 B rcd in 1847. Will leave it to you to find the parish - This is tedious.
For Martin O'Malley M 1870 +/- 1 yr somewhere in Ireland, I found 5 M rcds: 1869 Mayo, 1870 May, 1871 Galway, 1871 Mayo, and 1871 Roscommon.
For Julia Thornton M ditto, I found 0 M rcds. This is a NO MATCH to Martin's. The earliest M rcd for this name is 1878.
For Mary O'Malley B 1871 +/- 1 yr somewhere in Ireland with a father named Martin, I found 1 B rcd in 1871.
For Cummin " B 1875 ditto, I found 0 B rcds.
For Julia " B 1882 ditto, I found 1 B rcd in 1882 Kilcummin & Oughterard.
For John and Delia B 1884 & 1885 respectively with a father forenamed Martin, I found no B rcds in Kilcummin & Oughterard.
The only other possible sibling in this parish is Mark B 1873.
Rcd keeping in Galway and Mayo was generally late and sloppy.
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.