It can be tough getting a children's book published these days. Many publishers accept manuscript submissions only through agents. If you don't have an agent, you can't submit to them.
But, fear not. If you have a children's story that you feel is ready for publication, and you don't have an agent to represent you, I have good news. Mandy Yates, from the Children's Book Academy has posted a great list of publishers who are accepting unsolicited manuscripts. The list includes such publishers as Boyds Mills Press, Clarion, and Putnam.
Before you submit, though, remember to do your homework. Make sure your manuscript fits the needs and wants of the publisher you're sending it to.