One option, similar to what you're describing: use a green spotlight. In post production, create a chromakey using that color green. You can then replace it with black, dark gray, or any color you want. It will work best on white walls and clothes, and not very well when it's over something that changes its color (like a purple shirt or a vase of flowers). But even that might still produce a cool effect.

Depending on the effect you want, you also might animate (in post production) a "beam" that leads to the patch of darkness.

One option, similar to what you're describing: use a green spotlight. In post production, create a chromakey using that color green. You can then replace it with black, dark gray, or any color you want. It will work best on white walls and clothes, and not very well when it's over something that changes its color (like a purple shirt or a vase of orange flowers). But even that might still produce a cool effect.

Depending on the effect you want, you also might animate (in post production) a "beam" that leads to the patch of darkness.