[2][3] Greer played as a right fielder for the United States national baseball team at the 1967 Pan American Games, hosted by Winnipeg.

In the deciding game for the gold medal, Greer drove in the winning run as the U.S. defeated Cuba, 2–1.

Greer led the Kettleers to three league titles between 1979 and 1987, and managed several future major leaguers including Will Clark, Ron Darling, John Franco, and Joe Girardi.

[7] Greer served as the coach of the Davidson Wildcats from 1982 to 1987 and for the Wake Forest Demon Deacons from 1988 to 2004.

[12] Greer's wife, Becky, served as the superintendent of public schools in Radford, Virginia.