The sport of tennis utilizes a tremendous amount of core flexibility and strength. With this being said, a movement that I highly recommend in your cross training regime are cable twisting movements.
In my opinion, the ideal way to train the core, in this manner, is with a cable pulley. Do three different moves with the cable machine which has the arm that moves high to low. First, start with a “high to low” chop. Second, lower the pulley and do a “mid level to mid level” across your body. Lastly, lower pulley and proceed to a “low to high” motion.
If your training facility does not offer this machine, then use a “weight plate” and do the same three movements mentioned above.
Twist your way to a better tennis game!