There is risk in almost all sports. Each sports has a list of them.
One playing golf may have to worry about overexposure to the sun, or too much drinking at the same time becoming dehydrated from lack of water.
Boxing risks head injuries as does football, soccer, and even basketball and baseball but the risk is not as high in these.
Tennis carries repetitive use injury risk such as tennis elbow, wrist injuries, and even back and knee problems but most of these come from heavy use. If you don''t drink water you can become dehydrated and lack of a hat or sunscreen is a choice rather than a risk to overexposure to the sun.
Your risk of head injuries in tennis may come from a fall if you lose your balance, or maybe if you hit yourself with a racket. In doubles there is risk that a partner could run into you or hit you with a racket. But each of these is rare and improbable to cause an extreme injury beyond a bump on the head.
The risk is minimal on a tennis court for the type of head injuries that come with contact sports. I you want your kids to play a sport that limits head injury risk while at the same time giving them a sport for life this is the one.