Covington is a town in Garfield County, Oklahoma, United States. The population was 477 at the 2020 census. Covington is located in southeastern Garfield County. Oklahoma State Highway 74 passes through the center of town as First Street, leading north 9 miles to Garber and south 63 miles to Oklahoma City. Enid, the Garfield County seat…Covington is a town in Garfield County, Oklahoma, United States. The population was 477 at the 2020 census. Covington is located in southeastern Garfield County. Oklahoma State Highway 74 passes through the center of town as First Street, leading north 9 miles to Garber and south 63 miles to Oklahoma City. Enid, the Garfield County seat, is 23 miles to the northwest via OK 74 and U.S. Route 412. Oklahoma State Highway 164 leads southeast, then east 18 miles to Perry.