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 Bart(holomew) Cashman B ????, somewhere in Ireland, with a father forenamed Jere(miah), I found 0 rcds, anywhere at any date.
For Cat(herine) Cashman B ditto, I found two rcds, but these are too late for your timeline. This suggests that either their rcds didn't survive, or are among the 30% of rcds which haven't been transcribed yet. Suggest you wait until the database is more completely.
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.