DD's name is Caileen, an Americanized spelling of the Irish Caiolinn (sort of pronounced Kay-leen). Her nickname is Caili (Kay-lee) and one of the Irish women at our skating rink was very surprised to see that spelling. She said her cousin's little girl in Ireland was Caili, but that was the only time she saw it spelled like that here.
Other names (off the top of my head) are: Siorsa (Sorsha), Moira, Aine (Anya), Bridget, Morgan and Sinead (Shin-ade). Riley and MacKenzie are also popular with Irish...and some not so Irish...families. Olivia...I'm not sure if that is Irish...is also popular with Irish families. I will also add that all the Olivias that have been in my son's classes are incredibly cute, so I guess that is a good pick.
We had a great book when we were trying to pick names called Celtic Baby Names. It listed all original Irish baby names, plus Welsh, Scottish, Cornish and maybe a couple others.
Good luck!