Don't be afraid to get on a personal level with your clients. Chances are they're more nervous than you are! If your client seems stiff, take a moment to simply talk to your client. Discuss things that are personal and specific to them ("I love this jacket you are wearing! Where did you get it?") Anything to help them take their mind off of being in front of the camera for a moment.
Now I'm not saying you have to find out their life story and every intimate detail, but many clients just want to know you are more than just a person behind this camera clicking away. With children, this can be very important. Some can be very shy at first. As a teacher, I know that many times children feel awkward around strange adults until you show interest in something they're interested in. Don't be afraid of acting a little silly just to get them to smile. Your smile will probably make them smile! And don't forget an important asset you have at your finger-tips: the parents! Parents are usually more than willing to help you in any way. All you need to do is ask!