Traditional book marketing methods don't work very well for children's books. You'll reach some parents or grandparents who want to buy gifts for the little ones, but you'll never reach your fan base: the kids themselves. Kids who find something they like tend to become obsessed, wanting more and more of it. Reach those children directly and you'll get them to love your characters and get emotionally invested in your books. You have to be terribly consistent, but personal marketing to children can work better than any other kind of promotions.
When you communicate with kids about your books, your author persona should include some recognizable object. Tie this object in with the setting or topic in your books. The idea is to instill a recognition factor in kids' minds, so that when they see these items they'll think of your stories. For most people growing up in this country, a man wearing tennis shoes and a zip cardigan sweater brings an immediate memory of Mr. Rogers. Fred Rogers' branding was so strong his sweater is in the Smithsonian. Wear a funny hat, always wear a red sweater, insist on earrings that gaudily match the current book's topic. Make it obvious and never go without your signature piece when you know children will be around.
Contact schools within a comfortable drive and offer to give free school visits to promote reading. Have a plan and schedule so school administrators know you won't take up too much of their tightly-scheduled day. Practice your reading and acting by reading your book to children in libraries and bookstores. Bring props, demonstrations, puppet friends, or anything else that will keep the children's attention. Audience participation is key to getting a group of kids to stay interested.
Contact schools in farther districts and offer to give author talks to the kids via Skype Making a virtual presentation gives you more control, since you set up the environment, but it's harder to interact with everyone in the audience. Speak with teachers and administrators beforehand to clue them in on your presentation style and what they should expect from your time with their students.
Whether you're visiting physically or virtually, it's a good idea for you to supply pre-order forms for your books, and to have a good supply of the physical books on hand, as well. Design a fun and attractive order form that children can take home to give parents and offer as many versions of your book as possible. Even the most diehard eBook reader will often buy physical children's books, so arrange to sell paperback or hardcover copies, as well. If you're visiting the school in person, bring a supply of books for teachers, and consider donating a copy or two to the school library. After all, it's all about marketing and the more eyes on your books, the more sales you'll eventually make.
Keep the Faith and May the Force be With You!