Photographing children can be rewarding and challenging. It is 10% technical ability and 90% psychology. If I knew that my job, for the remainder of my life, would depend exclusively on photographing children - and - I was given a choice between the very best camera equipment or a complete understanding of the psyche of children, I would choose a shoebox and a strip of film.
There are a number of techniques that can be used to change the mood of a child. But why would you want to do that? You have a treasure chest of opportunity right there in front of you. You may be passing up the perfect opportunity for a wonderfully unique image.
Recognize his/her mood. Is your subject cautious, silly, shy or frightened? Is he insecure, frustrated, wild or crabby? Perhaps she's clinging to Mom. Or maybe she's sleepy.
Use his feelings to compliment the session. Don't try to change her personality to fit your ideas. Change your ideas to fit the mood. Once you have some beautiful images and gain your subject's trust, then you can manipulate the mood a bit more. But in the beginning, just go with the flow.
Photo credits: Aleksandra Belikova, Cynthi Kovach, Pavel Losevsky, Olga Solovei.