Curley Lambeau won six NFL titles with the Green Bay Packers (1929, 1930, 1931, 1936, 1939, and 1944) and George Halas won six NFL titles with the Chicago Bears (1921, 1933, 1940, 1941, 1946 and 1963).
Paul Brown won seven titles with the Cleveland Browns, four in the All American Football Conference (1946, 1947, 1948, and 1949) and three in the NFL (1950, 1954, and 1955).
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This statistic is through Super Bowl XLII: Chuck Noll of the Pittsburgh Steelers is the winningest coach in Super Bowl games, having won 4. Close behind with 3 wins is Bill Walsh of the San Francisco 49ers, Joe Gibbs of the Washington Redskins and Bill Belichick of the New England Patriots with 3 wins. There are 8 other coaches that have won 2 Super Bowls: Packers Vince Lombardi, Dolphins Don Shula, Cowboys Tom Landry, Raiders Tom Flores, Giants Bill Parcells, Cowboys Jimmy Johnson, 49ers George Seifert, Broncos Mike Shanahan. 13 different coaches have won 1 Super Bowl.
As of the 2010 season, Tom Landry of the Dallas Cowboys has the most playoff wins of any NFL head coach with 20.
If you mean in the NHL, it is Scotty Bowman. For other leagues and world events I have no idea.