simple , adverts. adsense after first post in forum , adverts in banners at top. If its a big forum and "PUBLIC" people will advertise on it , expand the forum . Look at
www.sitepoint.com for a idea of how a forum can be expanded to be more than just a forum. Donations are good but most people will donate a bit but on going donations are hard to get. if its got a good PR then sell text links on a menu or at the bottom. There are lots of ways.
But sorry to say if its private there is no chance you will get anywhere with adverts, donations, expanding or text links. Its got to be viable and a incentive there for advertisers , donators etc. Like advertisers the incentive would be hits , viewers, traffic (guests), members seeing it and lots more
Hope that helps
Adam