There are 4 US Post Offices in Douglas County serving a total of 2,943 residents equating to 736 residents per post office. It's estimated that approximately 4,697 packages are handled across the 4 county post offices annually. Douglas County is a county located in the U.S. state of South Dakota. As of the 2010 census, the population was 3,002. Its county seat is Armour. The county was established in 1873 and organized in 1882. It is named for Stephen Douglas, of Illinois."