Printers are usually designed to refuse to print whenever anycartridge runs out, to avoid damage to the print head. So there's probably nothing you can do unless you install a colour cartridge.
However there's just a possibility that your printer might allow you to print a mono document if you tell it in advance what will be heading its way. (i.e. use the print setting that would only print in black & white even if you presented it with a colour document). To do so, press Ctrl-P (or go to File>Print) and, when the print dialogue box appears, click on 'Properties'. Then look for a 'grayscale' print option.