When I was starting senior design (3 or so years ago) there were companies of all sizes that would offer projects to senior design students. This mitigated the headaches of (a) coming up with a feasible project on your own that might be rejected by the senior design committee and (b) worrying about how the project is going to be funded.
If you're really hitting a wall with this and this option is not available through your college, I would suggest trying to find a company (smaller will probably be easier) that has a small engineering project they need done. You'd have to make sure the intellectual property rights to the project are settled before you start, however. I'm not sure how your university specifically works but at mine the companies would have to make a settlement of around $5000 with the college to own all IP rights to each project they sponsor, but to my knowledge, no one ever had a problem with this.
Anyway, just a thought.