There are several ways you can be successful teaching young children to play tennis. First and foremost you have to make it fun. Make your sessions fun by playing all kinds of games. Challenge them to hit 5 balls without hitting the net. Give them points for hitting certain parts of the court. 5 points for close to the baseline, 3 for the service line, 1 for getting it over the net. If they are not that skilled yet and they are missing it or hitting it on the frame of the racquet reward them and give them points for making good impact on the strings.
Do not be over concerned with having your young tennis player use perfect technique at first. Concentrate on keeping them moving. Have them move side to side and up and back and on a diagonal. Have them hopping on their feet the entire time. Make sure they are not standing around and you are not being too critical in their form. If they are a raw beginner do not feed balls at them as they may have difficulty just making contact. Have them run to you and just drop the ball next to their racquet and have them hit it. This makes it much easier and gives them confidence quickly.
In the beginning, instead of having them play in the entire court have them play only in the service boxes. For a young child the tennis court looks like a giant field and they can get lost in that big an area. The USTA (United States Tennis Association) has recently started a program for 10 and under tennis where they set up a smaller court. Four courts can be set up on one regulation sized tennis court. The program uses special nets, racquets and balls. This lets the youngsters play on a court at the size that is comfortable to them. They will develop their game a lot quicker and have a lot more fun on the smaller court. Don’t force your child to play and have them leave the court on their own terms. Some days they will not want to play at all and some days they will want to play all day. Let them develop at their own pace.
So keep it fun, don’t worry so much about their technique, have them play on a smaller court, and don’t force them into playing. Keep these things in mind and your child will develop much faster and have a healthier state of mind.