Get in charge of a children's charity you are passionate about and then have a coloring contest with one of the characters in your book. Give out merit awards to everyone. Maybe the award congratulates everyone for "Creative Excellance using color." It might be a printout you made and copied at Office Depot. Then call and tell your local newspaper about the upcoming children's charity coloring contest event.
Some newspapers will gladly take it to print in the local newspaper. This is free advertising for you and helps promote you and your book. Other people who read about the event may want to get free personalized autographs inside the book copies you will be selling.
If this children's book marketing strategy is not to your liking, stay tuned for more creative marketing ideas.