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 Peter Tiernan B 1831 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 2 rcds: 1831 Leitrim, and 1832 Louth. Father's forenames were Peter and Nicholas respectively.
For Ann McRann B 1838 +/- 4 yrs, Co. Leitrim, ditto, I found NO B rcds for this name prior to 1865. This is far from your timeline.
For Peter Tiernan M 1859 +/- 4 yrs, somewhere in Ireland, I found 2 rcds: 1860 Sligo, and 1861 Meath.
For Ann McRann M ditto, I found 0 rcds
You will need exact DOB, parent(s) name(s), and/or placename(s) to pick which, if any, is 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.