Born in Albany, Georgia, Coachman dominated the AAU outdoor high jump championship from 1939 through 1948, but was unable to compete in the Olympic Games as they were cancelled in 1940 and 1944 because of World War II. In the high jump finals of the 1948 Summer Olympics, Coachman leaped 1.68 m (5 ft 6⅛ in) on her first try. Her nearest rival, Great Britain's Dorothy Tyler, matched Coachman's jump, but only on her second try. Coachman was the only American woman to win an Olympic gold medal in athletics in 1948.
Coachman also excelled in the indoor and outdoor 50 m dash and the outdoor 100 m dash. Representing Tuskegee Institute, Coachman also ran on the national champion 4 x 100-meter relay team in 1941 and 1942. Coachman is an honorary member of Alpha Kappa Alpha Sorority, inducted in 1998 during the sorority's international conference.