If your editor does not natively support saving as indexed PNG, you will have to perform a destructive (lossy) operation, called "quantizing". Gimp isn't exactly lightweight and I have never gotten ImageMagick to do that properly, so I used a tool, called pngquant. It can reduce the image to palette with desirable number of colors, up to 2-bit, with or without added antialiasing. It has full alpha support.
Note, that images with lots of details (lines with non-integer width, lines thiner than 1px, fine curves) may not be represented with 2-bit palette without extreme quality loss, so experiment with colors count if you are not satisfied with result.
Also note, that some editors (Inkscape by default, Illustrator with some settings) won't pixel-align image elements, so quantizing will be less efficient due to the way multiple pixels are used for representing single "original" image pixel. If the image is sufficiently small, manually realigning lines to pixel boundaries may greatly improve the quality of result.
EDIT: I have got ImageMagick to work as well. Unfortunately, results of quantizing are very bad, compared to pngquant. There is an extra color in palette (e.g. requesting 8 colors produces png with 9 colors); images have severe artifacts, compared to same images, processed by pngquant. 2-bit images, produced by ImageMagick, are completely unusable.
All of above was observable with antialiasing and without.