Hmm. Never been in the situation like that. I've always refused to get banished and managed to stay inside the city. Of course everyone attacks me then, so I just have to wipe 'em out
*Krhm* Can you lockpick the door? If I have to quess, I'd say you will get attacked anyway, if you enter the city, so lockpicking is an option even those guards will surely attack you. You can also try to kill those guards for a key or try to pickpocket them.
If you're looking a peaceful solution to enter, I doubt there's any. Except loading an old game of course.