I have the good fortune to be the only son of a famous children's book author, though she hasn't been discovered yet. The reason I haven't published any of Mom's children's books myself is that they contain color illustrations (she's an artist as well as a writer) and print on demand isn't economically feasible for color printing. I've given Mom three books about publishing over the years, the first was Jeff Herman's guide to which I'd contributed an online marketing article, the next was my own (free proofreading) and the last was Aaron Shepard's book "The Business of Writing for Children." I suspect she actually read Aaron's book.
Self publishing children's books is a really tough match for my print on demand plus Internet marketing model on both fronts. On the print on demand side, it limits the author to text-centric books with a limited number of black and white line drawings for illustrations. On the Internet marketing side, even if you're successful at drawing children to a quality website, they don't have credit cards. Attracting parents to a website with content written for children is pretty unlikely, and if the site features color graphics, they may expect any books you are selling will be in color as well. You can go the traditional route and publish short color books with hard covers on offset, but it's extremely capital intensive, and you'll have all the usual problems gaining access to distribution. I wouldn't recommend self publishing children's books on offset to anybody who didn't have a proven method of selling products direct through public appearances, fairs, etc.
Following my usual M.O., I turned to Amazon Power Search to get a feel for what's going on with print on demand books for children. I used the query:
subject: children and publisher: authorhouse or iuniverse or xlibris or publishamerica or lulu
to generate a list of books that Amazon has categorized in the children's subject, and included five companies that use Lightning Source to produce and distribute print on demand books. Whether these companies are subsidy presses, "self publishing companies" or something altogether new, the services they provide through Lightning Source are also available to any author who becomes a self publisher by purchasing an ISBN block.
Amazon generated a list of 2968 books in response to my query, which I next sorted by bestselling. At the moment, the top book is "A Butterfly in Winter" by by Tara L. Entwistle-Clark, published through Lulu and categorized as "Young Adult." About one out of five books on the list appears to be related to education or child rearing , and maybe one out of ten is miscategorized. The most popular target audience looks to be ages 9 - 12, for whom shorter to medium length paperbacks are common. Prices are uniformly higher than what one would normally expect to pay for books in this genre.
None of the books in current list had an Amazon sales rank in the top 10,000 and the list tailed off into the hundreds of thousands very rapidly. This indicates that none of the authors of these books are seeing a significant income from their sales through Amazon, and since few if any of them are likely to be stocked in stores, it doesn't look very promising as a method for making a living. However, self publishing children's books will certainly teach you about the publishing business and at least you'll have something to say in your next book proposal to your favorite children's book publisher. Just don't get conned into paying more than a few hundred dollars to a subsidy publisher if you don't want to become a publisher yourself, don't sign away any rights, and don't pay any additional fees for book promotion that won't help in any case. Also note that the Amazon list generated above doesn't include books from true self publishers who have their own press name, so there may be a few out there with some winning children's titles.