I think telling a child to say cheese when you're snapping a photo is probably the worst way to try and get a smile. Charlie's at the age where when I ask him to smile I get the goofiest faces. His natural smile just disappears. I have to catch him unaware to get a nice smile from him!
Say cheese to someone today and photograph them as they're saying it back to you. See what kind of smile you get from them. I think we need to find a better saying than 'Say Cheese' to get a good photograph. I find that saying "farts" to a child often works! They always break out laughing.