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 Marg(aret) Diskin B 1844 +/- 1 yr somewhere in Ireland with the father's forename unknown, I found 1 rcd in 1844, Co. Mayo. The surname Diskin surname is sufficiently rare (888 B rcds) that there are only (50) Margarets. Those close to this are 1837 GAL, 1842 GAL, and 1844 MAY. One of these MAY be for your ancestor - no guarantees.
For Pat(rick) Sullivan B 1842 +/- 1 yr somewhere in Ireland with the father's forename unknown, I found 101 rcds. You will need an exact DOB, parent(s) name(s), and/or placenames to choose which, if any, is for your ancestor.
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.