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).
Newtown is in Co. Waterford. Waterford's rcds aren't in this database yet. Either your town is wrong, or your parish is wrong. Assuming that Co. Cork is correct, I found the following:
For John Herlihy B 1827 (exact) in Co. Cork with a father forenamed Maurice, there is 1 rcd in Ballyhea parish. This MAY be for your ancestor. You may want to wait until Co. Waterford's rcds are added to the database. Then you can search for a 2nd John Herlihy there.
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.