I'm only aware of the singing sessions connected to the Fleadh, but you might contact Comhaltas directly (see their website) and ask about music sessions.

Otherwise there's a few musicians including a box player and a fiddler in Gerry's Thursday session in Kynes and they don't seem to mind anyone playing along with them--they're very friendly and great musicians.

Closer to town on Thursday there's a trad session upstairs in Devitt's pub, in Camden Street. A young crowd, some of them very good, and they don't mind people playing along. There's probably trad sessions every night in the Cobblestone, Smithfield and Donoghue's, Merrion Row that allow people to join in. There are sessions in other pubs but I'm not sure whether they are open to outsiders.

Don