Having played in Irish groups for more that 30 years, I found that if the music is good and upbeat, the audience will appreciate it. Fields of Athenry is dreary and sung to death, it only really works if the whole audience knows it and sings along. We always threw in many Scottish, English, Australian, American and Canadian and no one seemd to mind. Whiskey in the Jar is sung a lot but is always a crowd favourite, the same with Paradise Waltzing Matilda
Can the Circle be Unbroken
Nut Brown Maiden
Seven Old Ladies
Squis Jiggin Ground etc

There is a whole rake of song suitable for an "Irish" style show without having to do boring, sentimental types that may only appeal to a very small portion of the audience. My advice is to mix it up, keep track of requests and pick the ones that you can perform well and go for it. Don't forget a few instrumentals. Good luck.