Start a "Wall of Sponsors" website. Truly anyone, not just the very wealthy or those involved in publishing, can sponsor a book fair. In fact, the parents of your entire school can sponsor it themselves, they all just need to donate a small sum of money. Regardless, meet with a website designer who can create a basic but cheerful website design where people can log on and donate money for the cause.
Host a potluck party at the school. While it might seem counter-intuitive, use the party as an opportunity to rally your teachers and parents to discuss the upcoming book fair and the need of sponsors. Parents will be more open to becoming sponsors when they're sampling tasty dishes in a warm and welcoming environment at your child's school.
Make fliers that advertise your search for a sponsor, how it will benefit the school and kids and the tax benefits the sponsors will receive. Organize teams of parents and kids to walk around the neighborhood giving out fliers to local businesses, encouraging them to join. It's wise to have the kids go with the parents as the business owners can meet directly the kids who will benefit from their help.
Write letters to major book publishing companies like Scribners, Penguin, Scholastic and others. While receiving sponsorship from such massive companies might seem like a long shot, corporate sponsorship will be completely beneficial to your school.