Bailieborough is the name of 2 parishes in Cavan: one CI, the other PR. The fact that this name has survived in your family history suggests these ancestors were protestant. Unfortunately, protestant sects were notoriously lax in keeping B/M/D rcds. So lax, that the government started mandatory civil registration in 1864.
While there are B rcds for Peter, Michael, and Thomas, none have a father forenamed Peter. There are NO rcds forDenis.
I research the Irish Family History Foundation's database. It contains 12,700,000 surviving rcds for abt 70% 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 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).
The notes on data sources for Cavan are less than helpful. They don't list the start dates for any parish religious sects. Additional rcds may await transcription. Suggest you contact firstname.lastname@example.org for more info.
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.