I just wanted to put this suggestion out there....
If you believe they would say no to just giving the cat away, maybe you could ask if you could just "borrow" her for a week. Maybe that you just found out that cats are allowed at your place, but before getting your own you'd like to see how it works out/if you like it, etc. Chances are, at the end of the week if you told them how fabulous the cat was and how you really want that cat, it might be easier to get the cat from them. They might see how nice it is not having the cat, etc. Or perhaps they will have forgotten the cat by then.

Again, just a suggestion....