Look the thing that I know about car rentals is that you can only get discount if you are hiring a car for a longer time span at least a week or more.
If you are hiring it for few days, On what will you get discount?
There should be enough amount on which you can ask for a discount and that can only happen if you are planning a longer journey.
Although there are a lot of things that contribute to this fact that whether you will get discount or not:
The type of car hired:
If you are opting for a cheap car you will definitely have less chances of getting discount. If you opt for a big branded car they will give you some discount.
Advance booking:
If you are booking the car for hiring in advance there are chances that you will get discount as there are schemes that are offered by many car rental companies. There is a disadvantage of advance booking that if you cancel your booking you might have to loose some money that you have payed.