Depending on how much you want to stress it, you could do what I call "time dithering". You have a sequence of b/w images in several buffers. The first buffer represents pixels that are meant to be more than 50% black. The next represents 25% black. Then 12.5% black and so on. At each frame refresh you use the least significant digits in the system clock to decide which buffer to point at the screen. A pixel that should be x% black will be rendered black x% of the time. If it refreshes often enough then you've made whatever bit depth of color you were after.

There are many hacks that can be used to improve this method I just outlined. Eg instead of picking a new buffer every frame, you can decide "switch or stay" from the current buffer. Or even just change which ones are displayed in some predetermined repeating sequence.