I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are increasingly sparse, B4 1800 rare. I only search the existing database.
For Thomas Begnal (+variants) B B4 1860, I found 4 B rcds: 2-1835, & 2-1837 (these may be duplicates).
Google the Foundation's name to lead you to this database. Pls post your search results to my genforum msg.