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.
For William O'Mara B 1845 (exact), somewhere in Ireland, with the father's forename unknown, I found 4 rcds, all in Co. Tipperary.
For Thomas O'Mara B 1845 +/- 4 yrs, ditto, I found 48 rcds, with 33 in Tipperary.
For Ann O'Mara B 1850 ditto, I found 28 rcds, with most in Co. Tipperary - too many to easily summarize here.
This assumes the children were B in Ireland. Suggest you find them in the U.S. censuses to refine their DOB in Ireland.
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.