Probably much the same as (some of) my mother's songs, though she was nearly 20 years older, and not Irish (lots of influence from a generation or two before though). She used to sing them in an outrageous cod-Irish accent.

Poor Dog Tray- I used to beg her not to sing the verse where the dog dies.
Mother Machree.
If You're Irish Come Into The Parlour.
Where the Mountains of Mourne Sweep Down to the Sea.
Some farrago about "Her daddy called her Paddy for he hoped she'd be a laddie"
Come Back Paddy Reilly (often substituting Boggart Hole Clough for Ballyjamesduff).
Pride of Petravore.

Dozens of others- she was always singing, everything from the latest pop songs to hymns.