You can certainly pay an author and an illustrator a fee for creating a book that you that you plan to use in your program, and there is nothing to prevent you from asking for contributions to pay the costs of the book.  It is not much different from asking parents to contribute so you can purchase bats, balls, and bases to provide for your softball team.  This is a little bit trickier because you are going to pay the author and illustrator through royalties, which could run for a very long time.  But I assume that you are going to own the book and pay them only for copies used in your program or sold to others.  Be sure that your agreement clearly spells out how much, when and for how long these royalties must be paid.

If you do not intend to own the book, you might still be able to raise funds to support it if it will be a “non-commercial” book with educational content that is not likely to be written without your support.  This could be a Type C Fiscal Sponsorship in which you raise funds for a book (a sculpture or a film) to be written by a non-exempt entity or individual for an educational need in your community.  Even if you don’t end up owning the book, you might be able to collect royalties on its later sales to provide a longer-term administrative fee greater than you might collect at the outset.

In either case, you want to be sure that you are not using your charitable status to provide unreasonable benefits to the authors, but there are external comparables against which to measure your payments that should provide any protection you think you might need in assuring that your payments are not out of line.