Join an organization such as the Society of Children's Book Writers and Illustrators and make sure you mention your membership in the cover letter. Editors like to know a writer is serious about her craft and is taking steps to become a better writer.
Find a local or online writing critique group and share information about editors and publishers. Five people in a group means five times the networking and research, increasing odds of finding the perfect house to publish the children's book.
Attend conferences and talk to editors one-on-one as much as possible. Ask what they are looking for and take copious notes. Submit the children's book to them if they request it along with a personalized note mentioning the previous meeting.
Look for a publishing house that offers children's book critique services. Fix your manuscript after the critique and mention the professional critique in the cover letter.
Enter competitions with your book. Often winners are picked up for publication.