Try this:

http://www.gigguide.co.uk/Edinburgh%20Listings/edinburghthursday.htm

Not a particularly great weekend for singing, it seems (there are several out of town festivals, it's the start of the season). You might try the Dalriada session on Friday night, a mix of geriatric-acoustic and Scottish trad - Dylan and Eagles numbers regardless, the venue is superb, on the Portobello promenade.