Well, I never see computers monitors that have them, but I suppose if they did, you could do it at the monitor if they had color controls like the old TVs had on the front of them. Just 'dial back' the color until all it shows is shades of gray.
I wish you had mentioned this earlier. I finally got around to getting rid of a gazillion old computer system parts that I've been accumulating over the years. Two items were a monochrome monitor and an 8-bit ISA Hercules monochrome video adapter.