Once and a while I get requests from teachers about how they can apply for grants in order to afford an author visit. I'm not an expert on this topic, but I do know many teachers do this in order to afford the special and educational experience for students.
My feeling is that the kids should be in on the efforts in order to get them invested in the visit. When I've visited schools and the kids have raised the money, decorated all the hallways with art and worksheets from my books, and even created a special KATIE DAVIS PARKS HERE! sign (a thrill to roll up to that!), they are far more excited and involved in what I'm teaching.
You can brainstorm with them, with parents, and other teachers to figure ways to do this. I know some teachers host a book night, or something at Barnes and Noble and raise proceeds to go towards a yearly author visit.
Yes, there are grants. Follett has a 68-page document with suggestions and information on many different kinds of grants here. No matter what you do, or how you get an author to visit your school, it's worth every penny, and every minute of hard work (yes, it's work!) because the children will never forget it.