This company has a location in California. They have multiple locations, but who knows whether they have multiple cars. Perhaps they just have 1 Cobra replica and move it between locations.
Shelby Vintage Rental Cars | Imagine Lifestyles Luxury Rentals
I got a $99 deal (through groupon) for a 1 hour rental out of their New Jersey location that I reserved for two weeks from now, so if they actually only have 1 car, it may be on the wrong side of the country for you to rent it.
As you can see a full day cost $599. The 1 hour rate is not listed on their site. I don't know if you can just call them up and ask for a 1 hour rental or whether that was just a special deal through groupon.