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