Rivers, New MexicoRivers is a census-designated place in Catron County, New Mexico, United States. Its population was 28 as of the 2010 census. The community is located at the confluence of the Tularosa River into the San Francisco River.GeographyAccording to the U.S. Census Bureau, the community has an area of ; is land and is water.EducationIt is in the Reserve Independent School District.