I should probably preface this by saying I in no way whatsoever would like Rex Ryan to be fired. This is a completely theoretical scenario in which next season just goes down the toilet.
My personal pick would be Perry Fewell, defensive coordinator for the Giants for those of you not familiar. Fewell spent 13 years as a college coach (never head coaching though he did assistant coach one time) and has served 5 different teams in his NFL coaching career.
In 2009 after Dick Jauron was fired, Perry became interim head coach and led the Bills to a 3-4 record. As unimpressive as that sounds, the Bills previously were being demolished giving up at least 20 points in 5 of their 7 games previous to Perry taking over (they also lost 6-3 to the Browns in no small part due to the brilliant quarterbacking of Trent Edwards) and looked like the good ol' Bills we know and love. After Fewell took over, the Bills largest margin of defeat in 7 games was 7 (alright I lied they lost 31-3 to the Falcons but Michael Turner was still good then and Matt Ryan had a team that wasn't garbage) they stayed competitive almost ever game and looked like a legitimate NFL team.
Fewell's top 10 defense led the New York Giants to a Super Bowl win against the Patriots in 2010 as well and was considered a finalist for the Washington HC job (alright maybe that's not THAT impressive) showing there's a belief he could replicate his Buffalo success.
That's my case, who would you want to be the head coach in a post-Rex world?