One of the best books about Photographing children that I ever had, was if I remember correctly at 80 years, was written by a man named Josef Schneider. Did a search on the Internet and found a link with used books. Some first editions for $75, but IMO would be well worth it if you plan a business shooting children. Some are $5 to $20 maybe not in as good conditions, but a great bargain... for those who may be shooting relatives or their own children. There also may be other bargains available at Amazon used books or Half Bay, owned by
eBay. TO me it was priceless at the time, the best book on Photography I ever bought.
josef schneider: child photography - AbeBooks
Used his ideas for years and it resulted in some fantastic portraits, won contests with them. One won the NE Professional Photog competition.
It has been out of print for decades I bought it in the 50's, but you may also find one in a good Library.
Used to always shoot them in their own home, the best place as they are more secure there. One idea I used that _always_ got a good smile. Had a bulb release and would hole the bulb out to them asking them to hold the "ball." But would hold the tube stretching it with my hand in front of my face. Then, Id let it go so it hit my hand and Id catch it. It looked like it hit me in the face. Id jerk as if it had. They would laugh a little then smile. Id catch that smile it was always a good one and natural...
Sometimes Id ask if they knew my name, when they said no, Id say "My name is peanut butter" all kids like it and itd break the ice. Get a nice smile. Then Id say did you know my wifes name is Jelly? Another smile, and then Peanut Butter and Jelly go together... Be silly with youngsters, but with things that make sense and you get good shots.
Would also bring with me, toys they might not have seen, like little footballs, dolls, Barbie's, trucks, Train Engines, tools that would fit their hands. Moms like the shots of their son holding a shiny new wrench, etc.