Pigmalion by Glenda Leznoff is a picture book adaptation of Pygmalion with some nods, of course, to My Fair Lady.
Juliet wants to be in the play that's being produced at the local theater but she suffers terribly from stage fright. None the less she has the lines memorizes and manages to befriend the director. Through some careful planning on his part and perseverance on her part, she's able to further learn the role of Eliza Piglittle.
It's a cute book but more aimed at the parents than the children. I supposer there could be some children out there who have seen My Fair Lady. I certainly had as a little kid. It could, though, be used as a way to introduce children both to the musical and the George Bernard Shaw play.