The C63 has lots of torque and there's no true way of actually making the rear end not slide under acceleration, but with careful throttle control it is possible. I don't think tuning it will eliminate it as that is the nature of the car.
Here is the setting I am currently using for my C63, its not totally perfect as I'm still in the process of tuning it but the rear is a bit easier to control than stock.
my good friend has this car, and its the same in real life..
hense why he hydroplained the QEW in toronto and did a $24,000 repair job on the front bumper
I have this car and I left it stock without fixing the suspension but it is equiped with Full Customized.. It is fully tuned make 650's i think.. and I just bought an M3 CSL same as M3 E92 to compare if what performs better in tracks.. C63 AMG has a nature of sliding but it's true if you control the car, it's a great fast luxury car!
I've got a setup, for 800+ bhp that grips great with no downforce (wing ruins the look of the car) however it only works with racing soft tyres, sports tyres it can get twitchy if your not driving on the limit, I'll edit this in soon.