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 Joseph Sullivan B 1879 (exact) in Co. Cork with a father forenamed John, I found 0 rcds.
For John Sullivan B 1844 (exact) in Co. Cork with the father's forename unknown, I found 35 rcds. Your knowledge of an (ALMOST) precise DOB may let you choose which one, if any, of these rcds is for your ancestor.
For John Sullivan M 1878 in Co. Cork, I found 5 rcds: 2-Macroom parish, 1-Mallow, 1-Milford, & 1-Mourneabbey.
For Marg(aret) Timmon M ditto, I found 0 rcds. This is a NO MATCH situation. It implies the M rcds didn't survive or the rcds of it haven't been digitized yet. This applies to the Joseph Sullivan B rcds as well.
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.