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