I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are sparse, B4 1800 rare. I only search the 65% which are.
For John Tierney B 1871 +/- 4 yrs in Cavan, I found 5 B rcds: 2-1869, 1871, 1872, & 1875. The rcd for 1871 shows a father named John, not the Patrick you listed. The rcd for 1875 lists Pat(rick). This is a connundrum. Either your rcds or the IFHF's rcds are in error.
Assuming your rcds are correct, I searched for a Patrick Tierney marriage in Cavan. There are 2 M rcds: 1864 and 1865 (there are 33 for all Ireland). Both occurred in the RC parish of Drumlumnan. There are two Mary Reilly M rcds in 1864 and one in 1865 also in the parish of Drumlumnan. A view of the detailed rcds will reveal whether the marriage was to the correct counterparty. The M rcd which does (if any) will USUALLY list their parents' names.
Google the Foundation's name to lead you to the database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.