Coweta is a city in Wagoner County, Oklahoma, United States, a suburb of Tulsa. As of 2010, its population was 9,943. Part of the Creek Nation …Coweta is a city in Wagoner County, Oklahoma, United States, a suburb of Tulsa. As of 2010, its population was 9,943. Part of the Creek Nation in Indian Territory before Oklahoma became a U.S. state, the town was first settled in 1840.