If it is the sort of thing that attracts eyeballs, especially eyeballs of a niche market, then Sponsorship / advertising is probably a good way to cover costs. I've seen other suggestions for using adsense. You can make some money from it, but approaching one or two big advertisers directly is way easier. You will make more money and offering exclusive coverage on your site for the cost of your servers a month is a true bargain for them.
Also, there's a saying that I think is appropriate to mention here: "If you aren't paying, then you're probably the product". Facebook is a very good example of that.
I also agree with other comments that you can probably reduce your server costs if you hunt around.
