I want to print out a bunch of unofficial cards against humanity cards. In order to save ink, I want the black cards to be white ink on black paper. I have an HP desk jet 2540. Is there a way I can get white ink for it?
Nope.
However you could print all the black area leaving the white letters to show.
That should save ink! 
There are ink jets that use white ink now, but it’s confined to higher-end commercial use from what I can tell. Looks like the stuff is nasty to deal with due to the high pigment content needed for opacity, as in you have to drain it back out when you’re not using it and maybe even have to print several layers of it for a true opaque white.
I know in commercial offset printing, a solid white is difficult to achieve. For the few projects I worked on that required it, we ended up using white foil to get the look we wanted.
I tried this about 20 years ago.
Find a big bottle on black ink and figure out how to refill the cart.
No white ink for commoners.
You could call around and see if any local print/photo shops have the white ink option.
If you have to do this ‘mail order’ (look it up, children), make sure you specify the card stock to be used. You’ll want the same weight and surface finish as the white cards.
And that is where you’re most likely to run into trouble.
The white ink may be used only on glicee (photo finish) stock, and the printer may not accept heavy card stock.
I had a ream of very nice card stock - and the ink ran all over it.
Inkjets can be picky.
The easiest way would probably be to type it out on a type-writer with a correction strip and then glue it on to card stock.
If you know anyone who still shoots with film and develops their own prints, you could print your cards on a transparency, lay it on top of some photographic paper in a dark room, flip on the lights for a few seconds, then develop them in the chemical bath.
Those things are unfortunately rare to find these days though. Unless you wanted to go through the trouble of buying your own paper and chemicals.
Reimagine the black cards as a different colour; print in black on light grey cardstock, for example.
Or
Have the cards printed in a store. It will be their ink you waste instead of yours. It might not work out cheaper but it will be a fixed, predictable cost to you (20 cents/sheet vs ??? ink).
Or
Print black on white as usual, trim and mount on black cardstock.
Or
Print black on white as usual but add black border to the cards to differentiate them from the other cards.
Nm
There used to be a product that made this possible. Sadly, KroyColor hasn’t been in production for decades.
How many of these things do you need? Use a Laser printer - toner is pretty cheap.
Or, get white vinyl cut at a sign shop, and stick it to black paper, but that;s sure to be more expensive than some toner.
What are “cards against humanity cards” (official or otherwise)?
That probably doesn’t work well. I assume any model of “desk jet” printer works by spraying ink on the paper (as opposed to laser printing, which uses xerographic process). If you spray ink over a large solid black area, you’re going to get a little bit of bleeding into the adjacent white areas. If you have large black areas (the background) surrounding very small white areas (the text), the size of the bleeding area will be comparable to the size of the entire area being bled into. This will render the white text as faint, fuzzy, and maybe even largely obliterated. (Not to mention leaving you with soggy card stock.)
Modern laser printers, to the best of my knowledge, all use “write black” technology, in which a photosensitive surface (the “drum” usually) is exposed to light in the areas to be printed. This tends to have the same result when large printed areas surround small unprinted areas, with the light on the drum bleeding into the unprinted area.
It would probably come out awful even if you found white ink. Probably cheap these days to get it printed professionally, maybe even cheaper than the ink would be.
Printing black ink around white letters will work fine on any modern inkjet, with quality paper.
Inkjet paper is specifically designed to not bleed significantly, and so the white letters will remain crisp. It will use a lot of ink, though.
nm.
White ink is pretty rare, even in commercial printing.
This sort of reminds me of a thread from years ago regarding how a laptop projector can display ‘black’…
I haven’t printed any C.A.H cards, I dabble with the online version on the odd occasion though…
Try searching for ‘cmyw printing “your area here”’ I just turned up a couple of options near me…
Are you talking about the “print your own” option that the CAH website offers, or have you created your own answers that you’d like to add to the preprinted set? If the first, it’s likely actually cheaper to just buy the damned thing. If you want to cheap out, expansion sets are only $10, and still come with a pretty nice array of black and white cards. If you want to create your own black cards from your imagination, I’d say black cardstock cut to size and a cheap label maker (you can get ones that print white on clear tape, but it’s probably more expensive than the standard black on white tape).