I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. I also search a database @ IRISHGENEALOGY.IE. Records before 1863 are increasingly scarce and almost non-existant prior to 1800. In both databases, early B/M/D events either weren't recorded, or the records haven't survived.
For James McConnell B 1830 +/- 5 yrs, somewhere in Ireland, with a father forenamed William, I found 7 records: NONE are in Co. Monaghan. Visit the website to explore further.