One problem that you will probably face is that most of our hand-eye coordination is developed at very young age and it is hard to develop further once you get older. And because of that, most tools, games and programs will be geared towards toddlers and younger. However, there are things that can help.
First, the most important thing you can do is play more tennis (or whatever sport you are interested in improving) nothing can match the experience of the actual sport since you will not only be tracking the ball, but you will also get familiar with tracking the correct colored ball on the correct colored background with a racquet in your hand, etc. Also, it is most valuable to play with another person and not against a machine so that you are able to track the ball without knowing in advance which direction it will be traveling or what kind of spin there will be.
However, playing more tennis requires another player which is not always an option. Another possibility is buying a Reaction Ball which is basically a strange shaped rubber ball that you can drop on the floor or throw against the wall and it will bounce off at unpredictable angles and you try to catch it before it hits the ground. This will improve both your tracking ability and your reaction time.
Another idea is a very easy one: Play video games! Many video games, especially fast-paced first person shooters, can really test and improve your hand-eye coordination. If you are not into first person shooter games, almost all video game consoles have a wide selection of "whack-a-mole" type games that are geared directly towards increasing hand-eye coordination.
Finally, for a DIY answer, a common technique is to use the hammer and ball drill. To do this, you take a ball peen hammer and lay it flat on its side, then you take a tennis ball and bounce it off of the side of the hammer while holding the hammer in your hand. The goal is to be able to keep the ball bouncing off of the hammer for as long as possible without hitting the ground. Once you get good at that, you can start walking around while performing the drill, then move on to using a golf ball instead of a tennis ball. Finally, if you get really good, you can turn the hammer 90 degrees in your hand and bounce the ball off of the hammer head instead of the side of the hammer as demonstrated in the video above. Another added value to this technique is that it will also improve the strength in your forearm and grip which is beneficial for tennis as well.