Originally Posted by themitchmann
Agility drills and footwork patterns will be helpful for fitness as well as technique.
This is a good idea.
If you wanna focus on his fitness at this point use it as part of learning the game.
There is a tennis lesson thread in the tips section where TennisBalla shows a pretty good drill where he moves his student and yet is teaching at the same time. These are the kind of things I would do with a younger player so that they learn to efficiently move around the court.
Try to incorporate as much tennis movement or skills into it. Hitting the gym just isnt gonna really do much for a 10 yo. Let him grow a little than you can worry about things like core strength.