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 parish, 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 Kiely B 1815 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 8 rcds: 2-1813 Limerick, 1814 Tipperary, 1814 Limerick, 1815 Tipperary, 1816 Limerick, and 2-1817 Limerick. Father's forenames were John, Thomas, John, Thomas, Jacob, John, Patrick, and John respectively.
With your limited info, you will have trouble determining which, if any, of these rcds is for your ancestor. As a general rule of thumb, the first son was named after the father's father. The first daughter after the mother's mother, etc. You can find these rules by Googling "Irish Naming Tradition."
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.