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 Mary Redican M 1855 +/- 1 yr, somewhere in Ireland, I found 1 rcd in 1854, Co. Leitrim. This doesn't correlate with info in your post.
For James Tierney M ditto, I found NO corresponding rcd. This infers that the rcd for Mary is a false positive. The two MAY have married in America. Suggest you contact RC parishes in New Jersey for their marriage rcd. If this still exists, it will likely show their parents' names as well as placename(s).
For Mary Redican B 1834 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 9 rcds: 1830 Roscommon, 1833 Roscommon, 4-1835 Roscommon, 2-1837 Roscommon, and 1837 Co. Dublin.
For James Tierney B 1832 ditto, I found 35 rcds - too many to list here, but NONE in Co. Roscommon.
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.