I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
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).
Note 4 - Microfilms of parish church rcds are kept by the National Library of Ireland (NLI).
For James Malloy B 1873 +/- 4 yrs, Newport CP, Co. Mayo, with a father named Mic(hael), I found 1 rcd, 1873.
For Rose Malloy B 1870 ditto, I found 1 rcd, 1867.
For Pat(rick) Malloy B 1869 ditto, I found 1 rcd, 1869.
For Mic(hael) Malloy B 1864 ditto, I found 1 rcd, 1864.
For John Malloy B 1863 ditto, I found 1 rcd, 1860, Kilcommon & Robeen RC parish.
For Ju(lia) Corrigan M 1856 +/- 4 yrs, I found 1 Julia M 1854 and Judith 1856.
For Michael Malloy M ditto, I found NO matching rcds. It looks like rcds for this event didn't survive.
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.