Boating and Rafting Permits. Cliffs tower above a flat water section of the lower Yampa River. NPS/Jacob W. Frank. Boating and Rafting Permits - Dinosaur National Monument (U.S. National Park Service) High-use lottery applications will be accepted December 1 to January 31 each year. All applicants will be notified of results by mid-February via email. Low-use, one-day trips and any unclaimed high-use trips will be available for reservation beginning March 6, 2020 at 8am MST on Recreation.gov. Applicants must be at least 18 years old.