Children's music is a very specialized market. You'll probably want some sort of education degree and good political skills to move up in this area, as there's a lot of competition for very few jobs. Much of the children's music market centers around television shows, so New York or LA are your hubs of choice in this field. Many of these shows hire a team of staff writers. In this situation, you may have to come up with new songs every week and you might be on the production team as well. On the movie side of the children's market, publishing affiliates of the major movie studios (Disney's Lyric Street, Dreamworks, and others) may use staff writers to come up with some of the songs for kids' movies. In any field of children's music, start by specializing in an age group and expand from there. If you're not at home with finger-painting or food fights, this job is not for you. To write convincingly for kids, you must be a kid at heart.