Beachcomber ~ If you are using the bluegrass style of picking you may have some problems locating traditional tunes that would fit 3 finger bluegrass style. I have heard bluegrass bands play "Red Haired Boy" which is basically the same tune as "Little Beggerman".If you play the melodic style 5 string banjo there is a book by Harold Streeter "IRISH JIGS for melodic style 5 string banjo. It is a bit of a work out unless you are pretty good at tablature. The book I have was published by MUSICPRINT CORPORATION ~ Lewalt Publishing Co., l980.
Another book that has a few Irish tunes is "MELODIC BANJO" by Toni Trischka. This book was published by Oak Publications, cl976.
I play a few Irish tunes on the 5 string using clawhammer and the melodic style picking. They are a lot of fun once you get them worked up.
Cap't Bob