There are 2 US Post Offices in Rains County serving a total of 9,898 residents equating to 4,949 residents per post office. It's estimated that approximately 15,798 packages are handled across the 2 county post offices annually. Rains County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 10,914. Its seat is Emory. The county (and county seat) are named for Emory Rains, a Texas state legislator. In 1970, Recorded Texas Historic Landmark Number 10860 was placed in the county courthouse lawn."