As it is, normal daytime photographs print much darker than they
appear on monitors (since paper doesn't emit its own light).
They obviously won't glow in the dark, but if they are displayed under appropriate light, they don't have to print darker. If they print darker it usually means, that the display brightness is cranked up too much or that the prints are displayed in insufficient light.
I'm wondering how to print inherently dark photos without losing shadow detail entirely.
I am not sure if I correctly understand what you mean by losing shadow detail in this context. If you see the detail on your calibrated display in your editor with soft proof on and you are using good printer profile, the shadow detail should show in the print with any decent print/paper combination.
Or do dark photos just need to be displayed under really bright lighting?
They should be illuminated normally. The print lightness can be adjusted to the light intensity under which they are displayed (up to a point).
As others pointed out, use paper with high Dmax. These are usually the glossy and pearl types. If you need natural or matte paper, there are some with decent Dmax as well, like the Hahnemuehle Photo Rag. Dmax values or L values of papers can be found on the internet. Or if you print at home, get a few sample packs and give them a try. Or talk to your lab...
Type of mounting will also play a role. I would think that for example a night scene print face mounted on acrylic will appear visually more attractive than a glass covered one (especially with less expensive glass).