Pierre & Wigs have excellent comments! May I add one thing?
If your friend does want to improve you may try to get him to look at black runs this way: What makes a black run a black run, is usually the steepness of its' pitch. However, when skied at an angle, that steep pitch is now reduced to the steepness of a blue or even a green run.
Rather, than getting him to do short turns, try getting him to do long turns using the whole width of the run. This way he can control his speed, helping him overcome the fear factor. Start this out on easier, shorter and less steep blacks, progressively moving to steeper, longer blacks. Once the fear factor is mostly overcome, he will come to enjoy the steeper runs more and more.
Go back and forth from time to time from blue cruisers, to black runs, so he can maintain his form and confidence. Keep him over the front of his skis and make sure he continually uses good pole planting techniques. Don't push him too hard but keep him advancing on both blues and blacks. One thing, though, make sure the blacks are groomed so he has the opportunity for the most control.
If he is agreeable to this, commend him for wanting to get better, then commend him again when he skis his first black, them commend him again, then again and again. Just be sure the commendation is genuine, not just insincere flattery. (He'll see through that!)
I hope this works out for both of you. Why don't you post back in a few weeks or pm me and let me know how it's going.