Buckeye is an unincorporated community in Matagorda County, Texas, United States, located nine miles southwest of Bay City, the county seat of Matagorda County. J. W. Stoddard and A. A. Plotner, the founders of the Plotner-Stoddard Irrigation Canal Company, who were born in Ohio, decided to name the town after their home state. The water came fro…Buckeye is an unincorporated community in Matagorda County, Texas, United States, located nine miles southwest of Bay City, the county seat of Matagorda County. J. W. Stoddard and A. A. Plotner, the founders of the Plotner-Stoddard Irrigation Canal Company, who were born in Ohio, decided to name the town after their home state. The water came from the Colorado River and was able to irrigate 30,000 acres of land. A school was set up for employee's children and a post office opened in 1907. In 1908, train service came to Buckeye.