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).
Your "Cavanrhea" is likely "Cavanreagh," the name of 5 townlands in counties Monaghan, Tyrone, Londonderry, and Fermanagh.
Co. Monaghan rcds aren't in the database yet. Suggest you wait until they are. This may take a long time; be patient. As an alternative, you can include Co. Monaghan in your trip itinerary. Suggest you coordinate with the parish of Clones. Also, visit the General Register Office in Dublin for possible civil B/M/D rcds which survived the 1922 Four Courts fire.
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.