There are 2 US Post Offices in Donley County serving a total of 3,666 residents equating to 1,833 residents per post office. It's estimated that approximately 5,851 packages are handled across the 2 county post offices annually. Donley County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 3,677. Its county seat is Clarendon. The county was created in 1876 and later organized in 1882."