A right-hander, Coates pitched in Major League Baseball for the New York Yankees (1956, 1959–62), Washington Senators (1963), Cincinnati Reds (1963) and Los Angeles/California Angels (1965–67).

He was born in Farnham, Virginia, attended Lively High School, and was listed as 6 feet 4 inches (1.93 m) tall and 192 pounds (87 kg).

Coates was a member of the Yankee team that regained the American League pennant in 1960, but lost to the Pittsburgh Pirates in the World Series in seven games.

The Yankees got Coates off the hook by scoring twice in the top of the ninth to tie the game, only to lose on Mazeroski's home run off Terry in the bottom of the 9th.

Led by the hitting of Maris, Skowron, Mickey Mantle, Yogi Berra and Elston Howard, the infield defense of Clete Boyer, Tony Kubek and Bobby Richardson, and Whitey Ford's 25–4 season, the now-Ralph Houk-led Yankees (Stengel had been fired immediately after the 1960 World Series) won the World Series over the Cincinnati Reds in five games.

In 1962, Coates went 7–6 for a Yankee team that repeated as World Series champions, defeating the San Francisco Giants in seven games.

Traded away by the Yankees (for left-handed reliever Steve Hamilton) on April 21, 1963, Coates would pitch another 80 games for three MLB teams through 1967.

His record was only 6–7 with a 4.48 ERA and two saves after leaving the Bronx, although as a starting pitcher for the Angels on August 14, 1966, he fired a four-hit, complete game shutout against the White Sox, the fourth whitewashing of his big-league career.

He also put up several strong campaigns in the Pacific Coast League during his late career, including a 17-win season for the 1968 Seattle Angels.