Carroll - 1994 Jets, 1997-1999 Patriots, 2010- Seahawks
Belichick - 1991-1995 Browns, Jets (see my earlier note), 2000- Patriots
Parcells - 1983-1990 Giants, 1993-1996 Patriots, 1997-1999 Jets, 2003-2006 Cowboys
Schottenheimer - 1984-1988 Browns, 1989-1998 Chiefs, 2001 Redskins, 2002-2006 Chargers
Dick Vermeil - 1976-1982 Eagles, 1997-1999 Rams, 2001-2005 Chiefs
Allen was an assistant with the Bears. Holmgren was HC only with the Packers and Seahawks.
Schottenheimer took the Browns to 2 AFC title games and at least one with Kansas City. And I'll never understand how he got fired after going 14-2 with the Chargers. As a Browns fan, I get that Marty was not a great playoff coach. In fact, it is painfully clear. But you can't win unless you get in the playoffs and Marty got his teams to the playoffs consistently.
Parcells' success gradually declined with each team he coached. 2 Super Bowl wins with 2 different QBs with the Giants, 1 Super Bowl appearance with Bledsoe in NE, and AFC title game with an aging Vinny Testeverde, and no real playoff success with the Cowboys. I'm not mentioning to take anything away from Parcells - he was a great coach. He took over bad teams and made them contenders in 1-2 years.