Cooney was the home plate umpire in Game 4 of the 1990 American League Championship Series where he ejected Boston Red Sox pitcher Roger Clemens with two out in the bottom of the second inning after Clemens used profanity while arguing balls and strikes. While the Red Sox vehemently protested, Cooney also ejected Marty Barrett from the bench for throwing water coolers on the field. The incident caused a 15-minute delay in the game. At the time, the Red Sox were trailing the Oakland Athletics 1–0 and eventually lost 3–1, being swept in four games.