I find the best way for most children to respond to me in a positive way in front of the camera is to act as silly as possible. Essentially, I must let go of any pride and make a complete fool of myself… much like a clown. For some reason kids love seeing the photographer get hurt. If they throw a tennis ball at you and it hits you in the face and you act like it almost knocked you out, they will laugh out loud. If you ask for a high five and then when they slap your hand you overreact like they just broke it, you’ll get a great smile and laugh often times.
I just bought a clown horn like the one you see below. It is loud, obnoxious and really great for getting young ones to smile. Especially in the three to four year old range. Just keep it in your pocket and when they give you the high five honk it with the free hand. They will go nuts. Also, try honking thier nose while you give the horn a squeeze. They’ll love it I promise you. Just a quick tip that you might try to get your young subjects to smile really great for you. 
I bought my horn at a little shop where they sell halloween costumes and party supplies. Any kind of shop where they sell party supplies probably carries these. They are well worth the money.
