Stability for stability's sake is just stupid. The guy has shown no redeeming qualities as an NFL head coach. His play calling is horrific, his time management is possibly the worst I've ever seen in the NFL, he has no personality and no real ability to amp up his players. I have very little faith in his ability to coach up young players, which is something critical to this team. Literally the only advantage to keeping him is you have some stability.
Of the coordinators mentioned my favorites are:
1) Dennison: The Texas offense is truly a perfect fit for this team. They're all about play action and running the ball. The same thing this offense should focus on with Trent at RB. They manage to get Foster around 25-26 carries a game and still send a lot of carries Tate's way.
2) Fewell: I generally prefer defensive minded head coaches. Downside here is he'd likely want control of the D himself so Jauron may find himself without a job. On the plus side, nobody who is available out there has as much experience dealing with a talented D-line as he does. The Giants have a nasty defense when their secondary isn't gutted, and it's all because of how their line plays. Something that's looking like it will be a strength of this team once they manage to land one more starting caliber DE. The line looks really solid this year and that's with 2 rookies playing major roles. Add in Taylor and you have a intimidating, nasty, deep, defensive line. Fewell is certainly a guy who could take advantage.
There are others I like as well but those two are my favorites.