I have never been there but use Airnav to check on places. I usually avoid places with "jet" in the name or "Million Air" so in checking the reviews my first choice would be Landmark Aviation but I would call about the courtesy car ASAP
http://www.airnav.com/airport/KSAT
There is a good thing about larger than reliever airports and that is that you can get services, rental cars, etc well into the evening.
I just called Landmark (may not have answered with that name) and they have THREE courtesy cars (2 hour use).