Turn the stained drape around so the stain faces the window side of the room and not the interior. While you have to look at the inner seam of the drapes this way, it's less noticeable than a stain.
Put a piece of furniture such as a couch or end table in front of the stain. Select a piece large enough to hide the whole stain and not just a portion of it.
Tie your drapes at the side of your window. When you bunch them up, ensure the stain is hidden from view. Loop the tie around the drapes and tie it in place. You can use blinds or another set of curtains under the drapes to keep people from looking into your home.