Born in Laurinburg, North Carolina, Covington attended Laurinburg High School then transferred and graduated from Hillside High School in Durham, where he was a football star. He didn't begin playing baseball until 1950 but his skills caught the eye of Boston Braves scout Dewey Griggs. Covington was offered a contract and assigned to the Class C Eau Claire Bears in 1952. While playing for the Eau Claire Bears, he first met team-mate Hank AaronCovington roomed with Aaron and catcher Julie Bowers, who had played in the Negro leagues, at the local YMCA that season.