Cigar Aficionado had an interview with Coppola a few issues back and recounts that screen test.
It wasn't even a screen test, as I recall. Someone was sitting in the room with him suggesting the role, and he just started playing the part. He poured some water from a vase into his hands and smoothed his hair, and used black shoe polish in it to make it streak, then he put the tissue in his cheeks.
They thought he was cracking up, and then everybody met Don Corleone.
How fortuitous to have black shoe polish handy. This sounds like some story Slick Willy would tell. I'm not blaming the teller, its just that my skepticism wouldn't let it pass.