I have written about 8 childrens books how can I get them published on royalty basis ?

Answer 1

If you want to get royalty publishing, you need an established publisher -- not a vanity press, not a self-publishing company, but a regular publisher who will not only edit, illustrate, format, and publish your books, but will also market and promote them. That's where so many of the on-line publishers fall down. There's minimal promotion. Yes, they will list them with Amazon, but no one will order a book they know nothing about. So you aren't going to make much money that way.
There is a book called Writers Market which lists the 3,000+ publishers in the US and tells you what their requirements are.
Generally, for children's books, you can send the whole text in with an outline and a cover letter. If you want the text back, make sure you send a self addressed stamped envelope (SASE) that has enough postage to bring your text back home. If you don't want the text returned, state that in your covering letter, and send in an SASE for their one-page reply. They'll either thank you for submitting your manuscript, but regret that it doesn't meet their needs, or they will offer you a contract.
Don't send all eight of your stories in at once. Just one at a time, with the best one first.
Good luck to you!

Answer 2

Below just some I find and know nothing about them. This you need to research by reading and maybe contacting a Better Business Bureau in the State they located. Try searches of; Book Publishers, Children Book Publishers.