Publishing Children's Books

First, I will tell you to try Storyjumper.com but then it depends on what you want. There are various sites for making kids books. 

MyStorybook.com - Make A Kids Book Online

This site allows you to write a kids storybook by 

• writing text
• using our images or adding your own
• adding background scenery
• drawing
• Adding, moving, and deleting pages

It's totally free, then you can choose to buy a high quality eBook version when you're done.

If you want to publish a kids book PROFESSIONALLY

If you want to publish a kids book more professionally, it's not quite as easy. There is a common myth is that publishing a children's book is easier than other genres. If you just meant a fun tool to make a kids book (by yourself or with children), check outhttp://myStorybook.com


Other sites you might want to see include: storyjumper.com, storybird.com, bookemon.com and scribblitt.com

KidsBookMaker is for making books as apps and is available for download.
StoryBird allows you to use existing artwork to make stories.
You can make interactive kids books using MangoReader- Build And Inspire Audience With Amazing Stories and Earn Money

MangoReader envisions a world in which children can freely create and publish their stories and find a niche audience that appreciates, gives feedback on and buys their work.

The best site depends on your needs.
Do you want to make a print book, A Kids book as an app, A kids book as an online book/ebook or PDF etc. 

But, you can make a book for fun using MyStoryBook.  
Really depends on your goals but if you want to take advantage of the massive Amazon audience and platform, check out their relatively new:

Kindle Kids' Book Creator 

Research your options for self-publishing companies.

I narrowed it down to the following choices:

1. AuthorHouse
2. CreateSpace
3. LuLu
4. Xlibris

You can visit this link for some tips  called the 28 Simple Steps to Write, Raise Funds and Publish a Children’s Book