If there is a closet in the room and has the same carpet in the closet you can cut a small piece out of the corner and replace the stained spot with it (glue it in place).
I have used colored markers and just feather it in. I have bought the big set you can find at the the dollar store. It might take a combination of colors. There are usually more than one shade of each color. Test it in a corner first.
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