I have no problem with paying members getting something for their money, but a private forum seems counter-intuitive. I am not sure why that would be a benefit or something I would pay for. The purpose of a forum is to get maximum exposure to answer questions or get feedback, so limiting that seems to limit rather than enhance the experience.
I would pay for email alerts, a google like function where I can put in a subject and get an email with a link to the post, notifications of updates to my posts, or other alerts. Also, I would pay to have a favorite list so I can save threads that I want to keep up on, for easy viewing. Any feature like that would be great to have, and would be a real benefit worth paying for.
Sorry. Marketing guy here. Can't help myself