I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
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).
For Thomas Henry B 1857 +/- 1 yr in Co. Roscommon with the father's forename unknown, I found 1 rcds in 1856. The rcd is in Boyle RC parish. Father's forename is John. This MAY be for your ancestor - no guarantee. The next closest rcd is in 1859. A view of the detailed 1856 rcd SHOULD give the parent's names and other info.
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.