Would this ordinance be unconstitutional?

The man isn't soliciting. In order to be guilty of soliciting them he would have to be asking for something from them. He's not. He's giving them bibles. Besides, some parents might not mind someone giving their children bibles. For those parents that do mind, they can teach their children to avoid the man, and refuse the bibles. It's not your place to decide what's right for ALL children. Butt out.