The book I bought is
"Professional Secrets for Photographing Children" by Douglas Allen Box. I like it because it shows many different lighting situations, lots of them using natural daylight. I prefer natural light partly because it gives the truest colors and partly because it means I don't have to go buy lights and reflectors! It's not a technical book -- I think only about one sentence per page lists f-stops and apertures and the rest is on lighting and posing and getting the kids to do what you want.
The other books I used I got from the library and I don't remember their titles. I did a quick search just now on Amazon using words like photography, lighting, and portrait and got dozens of books that came up. Take a look and see which ones strike your fancy!
Hope that helps.