I searched the IFHF's online database at ROOTSIRELAND.IE. It has abt 19 million B/M/D transcribed records for MOST Irish counties.
For James Moran B 1835 (exact), somewhere in Ireland, with a father forenamed Patrick, and mother M, I found 1 record in Co. Limerick. The mother's forename for this record is M(ARGARET). There are NO records using the mother's forename of Jane.