No head coach has appeared in 6 Super bowls with one team. However, Don Shula appeared in 6 Super bowls as a head coach for the Colts and Dolphins.
Miami Dolphins in Super Bowls VI, VII, and VIII.
Dallas Cowboys, 8
Buffalo Bills in Super Bowls XXV, XXVI, XXVII, and XXVIII.
Who else? The Pittsburgh Steelers
Teams that have won back to back Super Bowl Titles are:Green Bay Packers - Super Bowls I & IIMiami Dolphins - Super Bowls VII & VIIIPittsburgh Steelers - Super Bowls IX & XPittsburgh Steelers - Super Bowls XIII & XIVSan Francisco 49ers - Super Bowls XXIII & XXIVDallas Cowboys - Super Bowls XXVII & XXVIIIDenver Broncos - Super Bowls XXXII & XXXIIINew England Patriots - Super Bowls XXXVIII & XXIX
The Steelers won back to back twice