I immediately thought of three good methods. All of them involve product promotions in one way or another, so hopefully, they will be available on your Facebook page.
Allow people to pay you, and in return, you will promote their website, product or brand on the Facebook page.
Promote products with affiliate links so you get paid for every sale made through your links
Use it to promote your product and get as many sales as possible
A specific example might be if you have a fan page for a celebrity, you can somehow sell products related to that celebrity. Most of these methods are very similar but slightly different, and you decide which method to use.