May I suggest a virtual (or physical) pre-paid Visa or Mastercard. These are often treated as credit cards by merchants, but funds must be on the card. Instead of a cash deposit, they will do a pre-authorization for a certain amount same as a regular credit card. When the car is returned, the pre-authorization will either be cancelled, or drop off after not being picked up after a certain number of days. It's essentially a cash deposit, but means that kiosk clerks don't have drawers full of thousands of dollars in cash deposits received or to return.
Not every car rental agency will accept them either.
I don't know how far away your holiday is. But if you already have an online wallet, it's quite possible you can get a physical card within a couple of weeks, or a virtual card within days. And since most car rental companies accept online bookings and payments, you should be able to attempt to book online. Your payment method will be declined if they do not accept such.
Your own bank may well offer a low-cost pre-paid "credit card", although expect that to take a few weeks, as it will be a physical card. And may or may not be accepted.
You can also spend a lot of time contacting car rental companies in advance to ask. While it is most convenient to get one at an airport kiosk, you will only get a handful of the companies renting in any given city. Often smaller players are more accommodating, but it might mean a pick-up from your hotel next day to go rent.
