Let me comment from experience in training lots of kids (read over 1500)...
The most important thing you can do with very young kids is two specific ideas: one which has been touched upon by others, that is developing hand-eye coordination, movement and tracking skills.
But the other one is the one that too many pros, parents and coaches fail at: they try to toss balls and hit balls with a racquet--and worse yet, on a tennis court, too early.
Because of the unfamiliarity of young kids to use strokes that don't require strength, they tend to use very poor technique to get the ball over the net because of this perception. Parents especially believe if they toss thousands of balls to their kid, that somehow through attrition the kid will develop strokes. No, they develop bad habits in attempting to get the ball "over the net"...on top of which, the parents reward the outcome instead of the stroke pattern.
Take away the net, the court and even the balls. Spend no more than 5 minutes a week in establishing good stroke mechanics without the distraction of hitting a moving ball. Using the PracticeHit is remarkable for this. When my daughter was 5, we spent no more than 20 total minutes over the course of six months, just showing her the footwork, swing pattern, hold and balance of hitting this stationary ball (that swings back and forth on a shaft.) Since the ball doesn't go anywhere, the child is not going to be concerned with where it is going and can focus on the stroke feel and establish the stroke pattern. When my daughter was 7, we went to the court and she had perfect strokes. The only thing at that point we worked on was the timing and aim, something that is easy to build on once the stroke is established.
In addition, we worked on tossing bean bags to her racquet, holding the continental grip and learning to meet the bag instead of swinging at a moving ball. This is the absolute best drill when working on developing volleys. At 10 years of age, my daugher has far better volleys than most adults and even better than some of the college players here in town.
You can teach scoring by tossing a stuffed animal or bean bag and scoring each toss caught. My daughter knew how to keep tennis score by the first day we did this and she worked on her hand eye coordination in the process. Also, this drill can be taylored to be harder or easier, thereby you can help the youngster learn to "come from behind" by helping them catch easier tosses if they are behind.
All these and more are outlined, of course, in my book Coaching Mastery. The fact that most of my students over the course of 35 years teaching, possessed average athleticism, yet most all reached high levels of skill with many becoming top-ranked players. This pattern of teaching allows kids to get as good as they want, allows a fun way to learn tennis young without burning out, and those who want to reach top levels have the best chance to do so.
By the way, my daughter also learned to play golf this way and has an equally good golf game. You can see her tennis on my series of articles called "Training an 8-year old" on TennisOne.
Hope this helps some understand what you can do (and what you probably should avoid doing!) with kids.
