You have three very proven NHL coaches out there.
Lavvy
DeBoer
Babs
Babs public image is tarnished but I don't have a problem with him coaching. There. Would be a 3-4 year shelf life, but given how PR sensitive the Rangers are, I'm not sure it happens.
DeBoer is a curmudgeon. Great coach, but not the most affable guy.
Lavvy would be a great hire. Best fit for the Rangers among the 3. Am offensive Torts. Same intensity and values. Question is how much time would he want off between jobs?
Only example of a guy coaching right after getting fired was Bruce Boudreau in California.