Have you checked Autoeurope, sixt & europecar? I would think that you shouldn't have too much trouble finding something in Tallin, although I suspect they don't have as much call for premium cars as other cities to the west.

Your friend might have more luck securing a car in St. Petersburg, Russia, and driving into Estonia.

I got a car through autoeurope for Croatia about a year ago, though it was an economy. Even though it looked like everything was set on-line, I had to jump through several hoops with the car company after arrival to be able drive it out of Italy into Slovenia & Croatia. None the less, I was able to.

JP