Does anyone have a good example/template of an illustrator contract that a self-published author can present to an illustrator when contracting art work for a children's picture book?
Try Dan Poynter's website: http://www.parapublishing.com. He has a wealth of free and paid resources, including contracts.
I recommend hiring the designer before hiring the illustrator. With the designer as "art director" on your side, the book trim size and printing options can be planned, then the appropriate illustrator brought in to accomplish your goals.
When the illustrations are procured first, your book designer is often left to "make lemonade out of lemons" and the resulting layout isn't as good as it otherwise could have been. (I'm actually working on a children's book right now with this very problem.)
My blog post here, including the comments, covers some of the details.