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 county, 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 James Forrest B 1863 +/- 1 yr somewhere in Ireland with the father's forename unknown, I found 2 rcds in 1863 Cork. Father's forenames were William and Cornelius.
For James Forrest M 1894 +/- 4 yrs somewhere in Ireland, I found 3 rcds: 1892 Kildare, 1895 Tyrone, and 1896 Kildare.
For Mary Caffery M ditto, I found 29 rcds, but none matching those for James. Therefore the M rcds for James are likely false positives.
Your post mentions Dublin. Co. Dublin rcds are in the database. Dublin City rcds aren't. Suggest you wait until they are. This may take time; be patient.
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.
Hope this helps. Good luck.