In my understanding there is no longer an available shuttle.
You can take Air Train for FREE to rental car locations.
AirTrain makes frequent stops everywhere around the airport: airline terminals, parking lots, hotel shuttle areas and rental car facilities. What's more, every AirTrain ride around the airport is free. The service operates 24 hours a day, 365 days a year.
Once you’ve landed, finding the best New York City airport car rentals is easy—the Air Train takes you right to Avis at Terminal C/Federal Circle. Avis’s JFK car rental counter is conveniently located just 50 yards from the train’s exit.
Customers arriving by flight - Please follow the Airport signs to the Airtrain to be transported to the Hertz facility located at Station Federal Circle. The train runs approximately every 6 minutes and can be boarded from all terminals.
Your Alamo rental will be serviced by National Car Rental, our Drive Alliance partner location. Please follow signs to the Air Train and depart at Federal Circle. Proceed to the first floor make a right and go to the National Rental Counter.
And many more rental companies gives directions to their locations via Air Train. I assume that they have removed such "Free Shuttle" service, since people were taking advantage of it. So unfortunately, you will have to take the Air Train.
Even, in order to take "Free" hotel shuttles from JFK, you will have to take the Air Train.
There is a wide variety of hotels and motels conveniently located near JFK – many of which offer hotel courtesy shuttles. To connect with a courtesy shuttle, take AirTrain to Federal Circle Station. The following provides the most up-to-date information on nearby choices.