I have some labels that consist of mostly grayscale objects and a single text object that is Red. I can't figure out how to make the printer just use black for the objects that can be printed with only black ink. What I have had to do is print my labels without the red object and select grayscale on the printer preferences and then run them through again with just the Red object. The ink cost per label goes from $.06 to$.0125 - almost a nickel a label. I print a lot of labels, so that is a significant amount. It seems like there would be a way to do that with CorelDraw - just tell it to only use black ink for everything but the Red object.
Are these check boxes checked, top default color management dialog, (try checking the preserve pure black) , bottom printer dialog color tab
Not sure if that will work but if not try using K of CMYK and for grays a percentage of K of CMYK for grays in your files.