So, naturally, you require 2 things:
1. a collection (array) of dates for which the car is unavailable,
2. a way to block those dates on the calendar (datepicker).
For the 1st point, you could maintain an array of dates, by creating the array and storing it in a string form in the Car record itself and updating/using it whenever required.
For the 2nd point, the $.datepicker method allows a few options to block selected dates. You can use your earlier-created array of dates with one of the datepicker methods.
I am myself not sure about which methods and what exact code, yet, but i know that this approach can work out for you.