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 Pat(rick) Tucker B ???? in Mayo or Roscommon, there are no rcds prior to 1821.
For Pat(rick) Tucker M 1821 (exact) in Roscommon, I found 0 rcds. The closest to your parameters is a Peter Tucker.
For Mary Reddy B & M in Roscommon and Mayo, there are no rcds within relevant ranges.
For John Tucker B 1848 +/- 4 yrs in Roscommon or Mayo with a father forenamed Pat(rick), I found 0 rcds.
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.