I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. B4 1840 rcds are increasingly sparse, B4 1800 rare. My search is limited to this database.
For Patrick Smith B 1831 (exact) in Co. Cavan, I found 2 B rcds. Neither showed a father named Thomas.
For Phillip Smith B 1830 ditto, I found 1 B rcd. The father wasn't named Thomas, or it wasn't listed.
For James Smith B 1822 ditto, I found 1 B rcd. The father WAS named Thomas.
For Thomas Smith M 1817 +/- 4 yrs ditto, I found 3 M rcds. A view of the detailed rcd MAY show the bride's name was Mary. Caution - Mary is the most common forename for women in Ireland. A match may be a false positive.
For Thomas Smith B 1785 ditto, I found 3 B rcds: 1781, 1784, and 1786. This assumes he was B in Cavan. When I extend the search to all Ireland, I find 31 B rcds. Note - at this early date less than 10% of Bs were rcd'd.
Google the Foundation's name to lead you to this database. Pls post your search results to my genforum msg.