How can I market a social networking site with a limited budget?
Are you on Twitter?
Are you on Facebook?
Are you a member of any affinity communities housed on the Ning platform?
If not, get crackin'! It's important for you to "fish where the fish are," that is, find out where your market hangs out online, start hanging out there yourself and engage them in an environment that is familiar and comfortable for them before you start talking about your new social network.
This responsibility is a full-time gig and should not be taken lightly. If done incorrectly (read: not authentically), your brand has the potential to leave a bad taste in people's mouths.
So, in short, instead of trying to target 10,000 people yourself, engage with 10 people and/or groups that share your target market, who each have a reach of 1,000+ people. You've probably heard of O.P.M. - other people's money? Well, this is something that I call O.P.S. - other people's social.