HI John
Without parent's names unfortunately there are no public records that might be available to help you.
The local graveyards do not seem to have published gravestone inscriptions either.
You could always write to the editors of 2 newspapers in local circulation in South Sligo - the Sligo Champion and the Roscommon Herald - and request that they publish your letters.
These newspapers also have Facebook pages.
If this is of interest in your letter/s you should give some indication why you are looking for information on Mary.
Regards
Tom