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 Mary Boyle B 1846 (exact), Co. Donegal, with the parents' names unknown (a VERY broad search), I found 0 records.
For John Boyle B 1848 ditto, I found 1 record. However, the father's forename is Charles. This infers: 1) it is a false positive, or 2) some of your parameters are off.