I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse and almost non-existant before 1800. Many B/M/D events either weren't recorded, or the records haven't survived.
For Mar(y,garet,gery) Friel B 1840 +/- 5 yrs, somewhere in Ireland, with a father forenamed Pat(rick), I found 2 matching records: 1836 Co. Armagh, and 1843 Co. Mayo.
I couldn't find a marriage record for Mathew and Margery anywhere in Ireland at any date.