All larger branded and local car rental agencies in Belgrade (Sixt, Europcar, Budget, Hertz,…) require a deposit on your credit card when you pick up the car.

Deposit depends on car group, length of rental, car rental agency, etc.

Deposit for a small car group (economy car group) like Opel Corsa or VW Passat is around 500€.

I suggest you to find a small local car rental agency and ask if the rent a car without a deposit.

If you need best rates and quality car rental company than you should book a car with car rental brokers like Arguscarhire, Rentalcars or even better through Belgrade Car Rental where you can choose among best locals and global car rental agencies in Serbia.