Used to be an Irish session at Pogue Mahons in Seel Street but I haven't been for a very long time so don't know if it still goes on. They could try phoning

You don't say what kind of session.

The Junction at Rainhill used to have a bluegrass session on Wednesdays but again it's a long time since I've been there.

Pity they won't be there Monday - good Irish session at The Edinburgh, Sandown Lane Wavertree.