Both destinations are served by Dehra Dun (DED). Since there's no flight route between them, the best way to travel is by road.
Rishikesh
Fly to Dehra Dun (DED), then travel by road to Rishikesh. Taxis, buses, and private cabs are available from the airport.
Dehradun
Fly to Dehra Dun (DED), then travel by road to Dehradun. Local transport options include taxis, auto-rickshaws, and state buses.