there's a bunch of songs that aren't really irish (hmmm....sounds like another thread) but ARE associated with Irish Pubs. The Garden Song, No Man's Land, and yes the dreaded Unicorn. I would do all three of these and all of the others mentioned in this thread. I would also consider the following....

the Rising of the Moon
Four Green Fields
Come Out ye Balck and Tans
Fare Thee Well Enniskillen
The Moonshiner
Mark Mack

btw, have a great gig!!!
Frank