Tennis requires a balance of speed, power and endurance. Conditioning is a major part of success because fatigue leads to sloppiness in form, which will affect every part of your game. Footwork and flexibility is very important and should play a special role in a training program a long with supplementation for joint health. I highly recommend practicing yoga once or twice a week. Increasing flexibility will increase velocity and power in your stroke.
When you watch a tennis player, you see the power moving up the entire kinetic chain. A push off the ground transfers to a coil in the core, that is then released with a snap through the shoulders, elbows, triceps and wrists. The reps and weights should focus on muscle endurance with light to moderate weights. The intensity of your work is what matters.
Monday (5 Round Circuit, 90 seconds between sets)
Power Clean 5×5 (light to moderate weight)
Overhead Press 5×10
Pull-ups (bodyweight or weighted) 5×5-10:
Hanging toes to bar: 5×15
Wednesday (5 Round Circuit, 90 seconds between sets)
Clapping pushups 5×10
Ball slams 5×10
Russian twists 5×20
End with this: Tabata jump rope (20 seconds max effort, 10 seconds rest, 8 rounds)
Sprints: 30 seconds max effort, 90 second rest for 8 rounds.
Box jumps 5×10
Jumping lunges 5×10
Underhand medicine ball throws 5×10