Children of certain age can suddenly lose the power to grin without looking like some weird gargoyle off a church! (In fact some parents do too!)
The tip to getting a genuine grin is to give them something they really laugh at.
Here are some things you can do
Be prepared to giggle yourself - and if needs be to wholly act the idiot.
Remember what TV programs really make them grin.
It's surprising how often Daddy doing something unfortunate works!
If they are old enough, do they tell jokes? Do they laugh at jokes?
For young children, if they have a preferred toy that can be used to make them laugh or giggle then definitely bring that along. I can also use it as a prop in the photos.
If they like a specific song or rhyme, then either bring it on your smartphone or be ready to sing it with them.
I like to keep things fun and relaxed with youngsters. I understand they exchange moods from moment to moment. I will treat them with respect and generally just let them play around so that the session is fun and not a chore. If they are happy and enjoying themselves the photos will reflect that.