Many writers submit to a publisher thinking they need an illustrator, when often it hurts the chances at acceptance.
Unless you make clear the writing and illustrations can be considered together, but also apart and should be accepted as two separate submissions. Rarely do combo submissions hit and the editor/publisher wants to keep people together, more often than not, one of the two submissions are weaker. If you're an established team, if both the illustrator and writer are working at the professional level, and if you're willing to let the other person be accepted while you are not, then learn what the publisher wants and submit just your own work (if YOU are the writer, illustrator, then make sure YOUR work, ALL of it is at a professional level, because both parts reflect upon each other-- an editor once told me she was looking for the reason to say "NO").
(CAVEAT: RESEARCH PUBLISHERS. If a publisher asks YOU for MONEY, proceed with caution. This isn't the way the business works, unless you're self-publishing; they don't have your best interests at heart, and may not be reliable. Ask others, Google is your best friend, and read the fine print. Make sure you know what you get for your money, and the publisher is known for delivering it. I will deliver this caveat every time I speak about publishing, but realize friends don't let friends drive vanity sales.)
Anyhow. Two other advantages editors have over self publishing is a wide variety of artists to choose from and editors sometimes think outside the box, as artists sometimes do. I mention this, because nearly as often as I've heard, "I wish I wrote-- I've got a children's story!" I've also heard "I wish I drew/illustrated-- I love children's stories!", and the true purpose of this post...
Perhaps you can...
NOT all illustrators paint. I'll list some of the more unusual illustrating methods. If you're self publishing, and need an illustrator, think about the character of your work, and the skillsets of you or people you know.
Pegi Deitz Shea and Cynthia Weill's Ten Mice for Tet comes immediately to mind. Not only were there two writers, but there are two illustrators: To Ngoc Trang and Pham Viet Dinh.
The collaboration was rather different in this case. First the illustrations were painted, then they were embroidered. Personally, I think the photographers should (and more than likely are in the colophon) credited, as well, because the special art projects take a certain nuance to reproduce well. The textures IN this book is AMAZING.
Or perhaps cut paper is something you enjoy playing with. My friend Denise Ortakales or Cathryn Falwell are wonderful examples of what you can do with such things (you can make calligraphy paste papers, origami papers, or any kinds of bits, what you can imagine, it can be)
And of course Lois Ehlert. Her career has been long and starried, but each book still has a wonderful individual taste.
Another surprise is Denise Fleming. Her art is a surprise, because though she calls her illustrations collages, and they are paintings, the paper is the art and the art is the paper. She creates her illustrations from colored paper pulp. Her most recent book shows the technical skill and level she's come to (anyone who has made paper knows what I'm talking about), and it's a very intriguing idea:
Christine Brallier is documenting her process of illustrating a children's book in mosaic. There's sculpting, bas relief, steam punk art. I have a sculptor friend, Michael Shaughnessy who works in of all things: HAY. Just like good writing, it's not so much the topic, but the expression behind it.
I write this not because I think you need a gimmick. And most definitely, the art should reflect the text, reflect the story, and speak to your reader. However, we get trapped into ruts of thinking, and often we forget we have unhidden talents hiding in plain site. Or know others who do. This is a post to just think of the possibilities.