Hi,
There are no baptismal records for Ballingarry for 1829-1949
However on the 12 June 1830 a William Fitzgerald married a Maria/Mary Sullivan in Ballingarry
Looks like that William died in 1880 aged 80, recorded as a farmer so unlikely to be your ancestor
and on 28 Jan 1831 a Richard Fitzgerald married a Maria/Mary H?????
You say she was classed as an orphan so presumably the parents died before 1850 when there were no records
Do you have any other information, mother's name?, sibling names ?, fathers Christian name, occupation ?