1. Each car has its own set of ATs running on the blockchain
2. User sends funds to use the car for a certain period of time
3. Upon receiving funds AT releases a key which 'unlocks' the car for that specified time period
Rather than "releasing a key" it would probably make more sense that the renter provides a "secret" and the hash of this would be stored in the day(s) they wish to hire (assuming perhaps 31 variables where one is for each day of the month).
When they turn up to pick up the car they provide the secret (which then clears that day ready for the next month) and if they don't turn up then perhaps something like a message with the hash from the AT creator clears those days (as a forced cancellation).
Note that with this approach each car would only need a single AT.
Also as blocks are not an exact measure of time each AT might need manual messages (from its creator) to keep it time locked (otherwise perhaps create a new AT every month or create ATs with 366 variables to cover an entire year for a car).
Assuming this a bit like Uber (but renting your own car out rather than acting as a taxi) then I think a key part is going to be having a smartphone app.