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 John Clancy B 1831 +/- 4 yrs in Charleville, Co. Cork, with the father's forename unknown, I found 1 rcd in 1828. Father's forename for this rcd is Michael. Assuming this is the right rcd, a view of the detailed rcd SHOULD show the parent's names.
For John Clancy M 1856 +/- 4 yrs in Co. Cork, I found 6 rcds: 1853, 1854, 1856, 1857, and 2-1860.
For Mary Cronin M ditto, I found 30 rcds - too many to list here. However, there are no matching marriage rcds for those of John in any Cork parish. They may have married elsewhere.
For Daniel Clancy B 1857 +/- 4 yrs somewhere in Ireland with a father forenamed John, I found 1 rcd in 1859.
For the remainder of the children, I can't find a consistent pattern. Note 2 may apply here. Suggest you wait until the database is more complete.
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.