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. By 1800, they are almost non-existant. Many B/M/D events either weren't recorded, or haven't survived.
Minnie is a RARE forename in Ireland. This is the 1st time I have seen it in several years of searching. More than likely, it was a pet name used by the family.
For M????? Hughes B 1877 (exact), somewhere in Ireland, with a mother forenamed Eliza(beth), I found 4 records: Roscommon, 2-Down, and Cavan counties.
For Eliza/beth Hughes B 1855 +/- 5 yrs, Co. Tyrone, with a mother named Mary and father named James, I found 0 records.