My DD is 28 months old, and very similar, in that she only would fall asleep nursing. I really didn't see how it could work...
I first tried the Pantley routine. Basically, you remove the nipple earlier and earlier until they learn to fall asleep without. That really just made her mad. But, I know it works for some people.
What worked for us was to just totally change our bedtime routine. Instead of nursing falling right before sleep, it moved to the front of the routine, after we got in bed, but before book and back rubbing. We talked about it a lot before hand. The first couple of nights, when she got too upset, I would nurse her for 10 seconds ( I told her ahead of time, and she was already familiar with this limit). It took about an hour with me laying next to her/snuggling the first couple of nights. Since then, maybe 10-15 minutes from the time our bedtime routine is over until I can leave the bed. We're trying to transition DH into the routine now, but so far without much luck. If he's there, it's time to play....
Good luck!