All the current cars work great on asphalt.
Recent carpet setups are so soft they will work on asphalt too. Just use Magenta or Pink tires all around.
The only real difference is traction compounds. You want to put on a high solvent traction compound (Paragon, SXT3) on first for 5-10 min then put a layer of runny sun tan lotion over it for another 10-20 min. Wipe the tires hard 5 min before your run. They may feel a little slimy, that's ok, they will stick. If the car is too edgy on the first lap or two wipe the tires later so they are wetter/more slimy when you put the car down. If you wipe too soon the tire will get really tacky and the car will be darty for a few laps until it settle in. If the tires are a little greasy/slimy the car will stay consistent.
How it works...The compound softens tires by partially dissolving the rubber. The suntan lotion has lanolin in it which bonds with the partially dissolved rubber and softens it more.
On Asphalt traction compound alone makes the tires too sticky and they will pick up dust and lose traction. Adding the suntan lotion somehow makes the tires self cleaning. If the grip is high you can use just suntan lotion.