I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 19 million B/M/D records for MOST Irish counties.
For Pat(rick) Flynn B 1866 (exact), Co. Tipperary, with parents' forenamed John and Mary, I found 1 record. I also found records for William and Mary on/near the DOB you stated.
For a John Flynn and Mary Murphy M in 1861 +/- 5 yrs, Co. Tipperary, I found 1 record in 1864. A view of the detailed record(s) (usually for a nominal fee) should affirm/refute whether these are for your ancestors.