As far as I'm aware there isn't a dedicated black and white inkjet printer on sale, and the cunning manufacturers are good at preventing you from printing at all when just one colour has run out even if its only one cartridge that has run out and not even the one you're printing with!
Not knowing what your printing requirements are its hard to suggest printers, but look out for ones that have seperate dedicated colour cartridges - that way you can just replace the one thats empty - and check there are cheap compatibles out there to keep replacement costs down.
Kodak printers have a dedicated black cartridge, but their colour cartidge is a combined cartridge so you could end up wasting ink if you print more of one colour.
Hope that helps!