If you are willing to do it the hard way, you can use standard black-and-white photographic printing paper and do a reversal processing on it. What that means is that you will be making a negative, but then making a direct positive from the negative without an additional imaging exposure (though there will be an additional exposure to light).
It will require some testing, of course, to determine the "ISO" of the paper and get a feel for the processing procedure, so you'll probably write off your first box of paper as the "entry price" into the Weird Photographic Processing Society. But it's essentially the same procedure used for creating black-and-white slides.
First, expose the paper in the camera, then develop to get a "good negative" and stop -- but do not fix. That will precipitate the silver out of the areas that you eventually want to remain white, and proportionally precipitate the silver elsewhere according to its desired lightness. Expose the paper to a uniform light source, which will turn the remaining halogenated silver into a latent image. Then bleach the silver (negative) image out with a potassium ferrocyanide solution, which will "reset" the silver that was previously developed out to halogenated silver (silver halide). Now you can develop normally, including stopping, fixing and archival washing.
You can probably expect some funky colour responses from this process. Single-grade black-and-white papers aren't sensitive to much of the spectrum, and will look an awful lot like 19th-century photographs. Variable-contrast (VC) papers are nearly orthochromatic (sensitive to everything but the red end of the scale), but the blue-sensitive and yellow-sensitive parts of the emulsion have very different contrasts.
You can also use a liquid emulsion (make sure it's for photography, not screen printing) applied to substrates of your choosing (handmade papers, textiles, boards, metal, etc). If you choose to use a liquid emulsion, then you also have the tintype option: a negative silver image over a black background looks like a positive (it reflects more light) so you don't even have to do a reversal. (It's a reasonable alternative to a Daguerreotype in an era where nobody will let you play with mercury anymore.)
