Hi, I had the same problem. But dont listen to the nay-sayers, it can be done!
I ordered a credit card specifically to hire a car in spain but it didn't arrive in time.
I contacted lots of companies, and had success with two.
I managed to book with just one days notice, a vehicle from Torremar Car Hire. It seems to be run by British Ex-Pats. They were perfectly happy to rent out a vehicle without a credit card. I paid with cash and used a maestro debit card as a security deposit. They met me promptly at Malaga airport and the car was waiting in the drop off zone outside.
I also had the offer of another car, from Dragon Car Hire, who, were a little more reluctant, but were kind enough to shop around to see if they could find me a vehicle. They found a car, but at such short notice, all they could offer was a more expensive class of vehicle. This is why in the end I went with Torremar.
I read this thread when I was searching for car hire, which is why I'm updating it with my information to help travellers in the future.
I don't personally like the idea of being told I have to have what is essentially a device designed for regular debt to go about my day to day life!