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 Thomas O'Malley B 1865-1870 in Co. Mayo with a father forenamed A(ustin), I found 3 B rcds: 1866 and 2-1870. None of these were in either Castlebar 1 or 2 civil parish. One of these is likely for your ancestor.
For Nora (Honor) Conwell B 1881 (exact) in Co. Mayo with a father forenamed Th(omas), I found 0 B rcds. Expanding the search range +/- 4 yrs met the same results.
For Austin O'Malley M 1867 +/- 3 yrs in Co. Mayo, I found 10 M rcds: 5-1864, 3-1866, and 2-1868. None are in Aglish parish.
For Elizabeth Walsh M ditto, I found 1 matching rcd in 1868 in Aglish parish.
For Th(omas) Conwell M ???? in Co. Mayo, I found 3 M rcds: 1846 and 2-1872.
For Marg(aret) McManus M ditto, I found NO matching M rcds. They may have married elsewhere in Ireland. Will let you chase this rabbit.
Rcd keeping started late in Co. Mayo for all faiths. Not too many parishes have rcds B4 1850.
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.