Although it is now off the air, I considered Conviction a great show due to my love for the Law and Order franchise. However, this show is definitely NOT for children due to its explicit sexual content (several sex scenes) and general scenarios that kids under 17 would not understand. If you do watch this show with your teens, there are some situations that will need detailed explanations (i.e. morality, honesty, sexuality, etc.)
This show isn't really for kids, but more, it isn't very good. There is too many plot lines going on with nothing major happening. I'd much recommend the other Law and Order franchise shows over this one.