Black screen means it absorbs everything. Because it's a translucent body consisting of a few layers, the light simply gets trapped within the layers and is not reemitted into our eyes. We perceive that as black.
If you want to make it whatever color, you need a not translucent screen, so the photons are partly absorbed and partly reemitted. Then we have some photons in our eyes and sensations that can be interpreted by our brain as information/color/whatever.
The screens of e-ink utilize that. But they're slow.
So to answer your question, no it's not possible to make ordinary screens to have a color, except there's a solid body in front of the layers to absorb and reemitt the photons.
To build a screen like that, one would need a backlight. No matter where it comes from. Or, inverted LCD on a white plane that alters the refraction when there's a current flowing. That would consume more energy because all the pixels need to be constantly powered (and after powering off, they would automatically alter their refraction..)
So, no..
What about constantly low powered screens like Samsung's the frame?
You can get monitors using those technologies if you don't want it to be black when off.
I imagine a black back on the screen improves contrast when it is on, as well.
Guess I’ll throw a nice colored cloth over the screen when it is off for now :)
Thanks for the Daylight Computer link!
(And also, there are color e-ink devices in the wild now, like https://us.kobobooks.com/products/kobo-libra-colour or https://remarkable.com/store/remarkable-paper/pro)
I’d love a display that let me pick the color or picture showing on the screen when it is off, or maybe it’s the wrong question and power-efficient things with solar panels directing sun energy to batteries that keep them going on all the time is the way.
To make them go white, they actually have to use power to clear the image. If you just let it sit there and let the battery die, the image will be there until you recharge it and turn it back on.
E ink is really cool tech (just patented and expensive). But the daylight computer from the other comment might be more what you're looking for.
And yeah you can totally run a solar setup. Anker makes a bunch, for example, of portable li ion batteries that can be directly connected to their solar panels.
Edit: If what you want is a digital billboard or picture frame, there might be some of those out there too, or I think I saw some DIY projects building those out of eink panels and an Arduino or such. Some of them get commercialized on Kickstarter.
I’m excited for the future with solar, battery, and really most electronic technology becoming cheaper and simpler.
And for some use cases, placing a sheet of white paper over the display might be good enough. Good luck.