The only red amethyst I've ever heard of comes from the Orange River in Africa, and even those specimens are not really red. They do, however, contain a nice layer of blood red hematite which coated the crystal during it's growth, giving it the appearance that it's red amethyst. But if you crack the crystal open and examine it, you'll see that the hematite forms a separately distinctive and relatively thin layer within the crystal (just under the outside layer of quartz). The hematite did not actually bond to the SiO2, such as is the case with the trace elements responsible for the coloration of amethyst. As for green amethyst, same deal. You might find amethyst with green inclusions such as chlorite phantoms or acicular actinolite but you won't find amethyst that is green due to atomic bonding. Black amethyst is probably just regular amethyst that has been naturally irradiated by the earth for a long period of time resulting in what is known as smoky amethyst. I've collected thousands of these in the western-most portion of the Basin and Range province and some of them have been so irradiated that they indeed appear to be black until examined with an intense light which brings out the purple.