I actually think being deadlocked in a war with the AI is helpful on occassion. If he is busy suiciding all his shiny new units on your city guards, then obviously he isn't concerned about building up his infrastructure. Granted, I play a little higher than Noble, but even still, just because you are in a long war doesn't mean you won't win.
Slug it out, only attack when the odds favor you, and try to flank his main force and raze/capture a city or two. He'll be paying you an indemnity before you know it. Also, please note that the AI won't negotiate unless some minimum number of turns expire or they have good reason to (losing cities and large armies is a good reason).
And when are your cities "too well defended"? I wish I had that kind of comfort level! The question is, are you varied with your defenses? When I have a border city defense force, I have a couple city defender longbows, granted, but I also assign a knight, a pike or two, and macemen/crossbowmen (I don't know what era you are in, but this is a good example). These units are promoted with combat and shock, or double combat and formation, or some other "offensive" combo. I'm always ready to go out in the field to fight my attacker off, not just sit behind my walls and watch him pillage everything in sight.
