You want to drive in Buenos Aires? Are you mad? Seriously why would you want to, the transport is so cheap, and the roads so dangerous.
If you are intent on still driving try "alquiler coche Buenos Aires" search in google. There will be hudreds of hits, although I can give no recomendations, at least you can then compare prices.
After renting - VERY expensive in Argentina - and borrowing a neighbor's car a lot, I broke down and bought a car at the beginning of the year. Yes, it's unjustifiably expensive, given all the cheap public transportation and taxis. And driving in the capital ain't easy, but then I'm used to driving in New York, which differs mainly because the average car is substantially larger there and harder to weave in and out of traffic. (And almost impossible to create a third lane of traffic where only 2 are marked!)
If you decide to buy and want advice on the local drill, drop me a line.
And if you find a leasing agent, please publish the info. If would be good to have as a reference.