I've found the followinglisting on FamilySearch.com:
Elizabeth Margaret PRIDAY Sex: F Birth: 06 Nov 1873 Waterford, Waterford, Ireland Parents: Father: James PRIDAY Mother: Bridget MC AULIFFE
If you haven't already, you should go to your local family history center and order the microfilm which contains this listing. It might give you some new info.
Do you have any idea of why your James came to Ireland? My Priday roots seem to be based around the area of Athlone in Co. Westmeath. I have been told that all Priday/Prydee/Priddys in Ireland can all be traced back to one common ancestor. But your James seems to be an exception to this rule.