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 sparse, B4 1800 rare. I only search the 65% which are.
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For Catherine McGauran B 1873 with a father named Mathew, I found 0 B rcds in Cavan and in the rest of Ireland.
Google the Foundation's name to lead you to the database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.
Hope this helps. Good luck.