I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 30%.
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 Elizabeth Breen B 1850 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 6 rcds: 1847 Dublin, 1849 Down, 1849 Tyrone, 1851 Derry, 1852 Dublin, and 1854 Tyrone. Father's respective forenames were Joseph, John, John, James, Thomas, and Rob(ert). Note - from your response to another post, you mentioned Boherbue as a possible origin. Rcds for this area haven't been transcribed yet. If your ancestor's rcds are among these, then all the above are false positives. You will need an exact DOB, parent(s) name(s), and/or placename(s) to pick which, if any, is the correct one.
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.