I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 20 M church, civil, census, etc records for MOST Irish counties. Records before 1863 are increasingly sparse - almost non-existant before 1800.
For Mar(ia) Hughes B 1857 +/- 2 yrs, Co. Monaghan, with a father forenamed Peter and mother Marg(aret), I found 1 record in 1857. This is likely the record for this ancestor. A view of the detailed record SHOULD reveal details to confirm/refute this conclusion.