How can I get my HP printer to print in black and white only even when one of my color cartridges is out?

I don't think there is any way. A color printer wants all colors available or it won't attempt anything.

There may be a work around option via the front panel setup. It may not be a black only, but it may be an option to continue printing regardless of whether one of the toners is being reported as empty. So, if what you are printing is black on white paper, and if the magenta toner is completely and actually empty, it should still print as back.

Our experience is that there may be hundreds and hundreds and maybe thousands of pages worth of toner still in the toner tanks even though HP wants to shut you down.

My reference is a HP-4700, but I think it also worked for other HPs we previously owned. The how-to details are in the million page owner's manual somewhere with the lead in being about overriding HPs toner limitations. I would imagine the there would be a similar override for ink jets.

There should be a setting in your printer's app that you can toggle between colour and black and white.

Check the print preview page carefully.

Don't have a solution but there's this guy on youtube that does videos only about printers. Found him very informative and thorough.

What's a magneta cartridge?

Some printers have a workaround for printing in black only when colored ink is out. As a minimum you have to turn off color in the print config dialog; with some printers you have to do more. And some just insist you buy the ink before they let you print at all.

Google with your printer model number and "print black only". It's worth a try.