You might contact your state board of education - to see if they can recommend providers or programs for autistic children. Since after school providers have to be state certified - or at least by the board of health - they might be able to provide you with some guidance.

It's difficult to give you a "one size fits all" answer to your dilemma, because I know that every child is different, even if they have the same diagnosis. Many parents with special needs children either use their own vacation days to coincide with when their kids are off of school, or they rely more on family to provide care, but if you don't have family nearby, then I wonder if you might approach some of the other parents of your son's classmates, and see if they might be willing to provide daycare during school breaks? (They are already familiar with having special needs children, and your son will already know their child.)
Perhaps you could see if any local college that offers special education as a major would have some students who are interested in working over the holidays, and could babysit your son?
Another suggestion is to contact local support groups, like www.autismspeaks.org or www.autism-society.org, and network through those parents to find out about appropriate resources in your area.
I also invite you to join Greatschools Autism Parents Group at community.greatschools.net/groups/18940