The award is given to the head coach who has "contributed the most to his team's success."
Ottawa Senators coach Paul MacLean won the award last season.
Babcock helped lead the Red Wings to their 23rd straight playoff berth despite a slew of injuries to the team's veteran players. Cooper guided Tampa Bay to a second-place finish in the Atlantic Division with 101 points a season after the Lightning finished 28th in the league standings.
Roy, in his first season in Colorado, guided the Avalanche to 112 points, matching a franchise record in wins. The Avalanche were just the first team in 35 years to finish in the top three in the standings after finishing in the bottom three the season before.MUIR: Top Line: Can Bruins stop P.K. Subban?; Wild’s big dogs asleep; more links