Let's assume the sun is at the zenith.
car width: 1.8 m
cabin length: 4.0 m
cabin area: 7.2 m2
sunlight specific power: 1000 W / m2
sunlight total power: 7200 W
On one hand, the COP of the compressor is probably around 4, meaning 4 watts of
cooling power require 1 watt of mechanical power, but on the other hand, the
engine's efficiency is about 25%, meaning 1 watt of mechanical power requires 4
watts of fuel burning. So we are back to square one, and require 7.2 kW of
additional thermal power to run the AC.
On a typical mixed city/highway trip, the average speed is 30 km/h, taking into account the time spent at stoplights. At 7 liters per 100 km consumption
without AC, this is 2.1 liters per hour. One liter contains about 32 MJ of
energy, and therefore, thermal power is 18.7 kW. The AC requires 7.2 kW more.
This means 38.5% worse fuel consumption due to AC if the car is totally black,
when compared with a totally reflective car with mirror surfaces.
On short trips, the black car can be even more worse, due to the fact that the
cabin air is already very hot. However, on long trips, you probably spend more time on the highways, meaning average speed is higher, and thus, the problem of additional fuel consumption caused is lower.
Of course, it may be possible that the car's AC system hasn't been rated to operate in the worst possible condition, sun at the zenith. So, I'm not claiming that when the sun is not in the zenith, the AC would cause 38.5% additional consumption always. And when the sun is at the zenith, if the AC isn't rated for this job, it will be a hot cabin and less consumption increase.
I can only conclude: don't buy a black car!