Probably the simplest way is to mix a dark grey from black and white and then add in a few dots of something to tweak the colour in whatever direction it needs to go - just looking online and images of greatcoats show a big variation in the basic colour, from blueish to brownish.
It's very likely even when new the colour of the cloth varied enormously - multiple manufacturers, no consistency in dye recipes - and add to that the effects of sunlight, rainwater and general wear and tear and you can go a lot of different ways. Just keeping it low-key enough is probably the only really important thing.
Einion