Some of the gyms I’ve been to have bulletin board where people can post if they want a training partner. Most don’t, thought. I agree with WolBarret that your best bet is to go to the gym regularly, and see if there are people there who are as dedicated as you are. Then ask if you can be their training partner. You could also ask some of the staff at your gym to keep an eye out for other people who want partners. I’m sure that it’s not an odd request.
The easiest way, of course, is just to grab a friend. My training partner for most of college was one of my roommates.
Random Aside: This sounds almost like asking someone out on a date. Imagine:
A: Say, could you give me a spot?
A: Thanks, that helps a lot. Say, are you doing anything Wednesday lunch?
B: Hm, why do you ask?
A: Well, uh, I was wondering if you wanted to, y’know, go to the gym together.