Why do blacks have green tones?
The green cast in dark black tones can be reduced, but only by cranking up the magenta so much that the rest of the image (skin tones in particular) gets very bad. You can do a test print. Make a 20:1 wide:tall aspect ratio horizontal grayscale ramp. Print it the width of your paper at the top of the page. If it’s tinted green, add magenta, and so on for the other primaries Repeat by printing farther down on the same piece of paper. Five or six iterations should do it, and — until you change type of paper or ink — you’re all set. Total expense: Half a page of paper and the corresponding amount of ink. Each print has to be should be separately proofed.