Try Resolve. It's a fabric and carpet cleaner spray that you can find in the household cleaner section of most stores.
You could also try putting some eye makeup remover on a cloth, rubbing that on the stains, and then ';rinsing'; with another cloth that just has water on it.
Good luck.How can I remove eyeliner stains from my carpet and couch?
Many beverages, medicines, cosmetics, foods, and other liquids contain dyes. These dyes may be absorbed into the fibers making removal very slow or impossible.
Go to this website for step by step cleaning procedure
If removal does not appear to be possible, call your carpet cleaning professional for advice. Sometimes the stain can be hidden by spot dyeing, retufting, or by repairing the affected area.
Sounds strange, but pantene clarifying shampoo probably would do it, it has a degreaser additive. Try a small spot first. Otherwise, try a foaming make-up remover or mild dish soap, not an oil based one.
Try any eye-makeup remover. Dab a little on the spot - don't rub. Wick it up with a clean dry cloth.
Most eye makeup removers are oil-based. If the remover leaves a dark wet-looking spot, dab that spot with a little dishsoap.