Dan,
Not busy on Friday evening, and in Central Manchester -- that's a hard call.
You could try the (trendy) Castle Hotel on Oldham St and see if it's back room is available. The Crown and Anchor on the junction of Oldham St / Swan St / Gt Ancoats St is a quieter pub but may not have the space.
Cornerhouse on a Friday evening upstairs, as just recommended, but I'd recommend that you need to reconnoitre and assess space and noise volumes.
As the Unis are not in session up you may have better luck slightly out of town, eg upstairs at Kro in the Uni Manc area (near Oxford Rd and Dover St).
mark