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