You can try and get your site sponsored by someone, But then you'll probably need to have ads on it, as well as links back to them and such.
Also, if you really want to do this, the student council should have enough funds to pull it off by themselves.
I know that I will probably get answers saying no, but it's worth a try. Are there ANY free .org domain names out there? I run the student council's website for my school, and they won't kick in any funds to get a domain name.