Children are naturally photogenic. I've worked in studios and children are so easy to photograph. What I hear from parents is that they don't think that their kids are that easy to photograph. This is only because they don't know some basic tips.
1. Young children especially infants take beautiful photos while they are asleep. Keep the light natural avoid flash if at all possible. Keep the image tight on the child and crop out distractions. For infants when they're awake you're better off having another person in image, it gives the child someone to interact with and you can crop the shot to keep the other person out of the image or you can keep the adult and child in the photo.
