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).
Note 4 - The National Library of Ireland (NLI) has microfilms of parish church rcds.
For James Tierney B 1842 +/- 1 yr, somewhere in Ireland with the father's forename unknown, I found 16 rcds: 1841 MAY, 2-1841 LIM, 1842 LEI, 1842 TIP, 1842 KIL, 1842 CAV, 1842 LIM, 1843 TIP, 2-1843 ANT, 2-1843 TYR, 2-1843 KIL, and1843 LIM.
For Lucy Grey B 1843 ditto, I found 0 rcds.
For Lucy Grey M 1864 +/- 2 yrs, somewhere in Ireland, I found 0 rcds.
Note - Lucy is an extremely rare forename in Ireland. Are you sure this was her name?
For James Tierney M ditto, I found 5 rcds: 1863 TIP, 1863 GAL, 1864 ANT, 1864 CAV, and 1865 MAY. Since they didn't have children with them, the 1865 Mayo rcd has the highest probability of being the correct one.
You will need exact DOB/DOM, parent(s) name(s), and/or placename(s) to pick which, if any, are the right one(s).
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.