Dampen a clean white cloth in paint thinner.
Test the paint thinner by rubbing it for two to three minutes on a small hidden spot on the furniture to make certain the thinner does not discolor or remove the finish.
Bunch up the cloth so the point on the tip is about the same size as the nail polish stain.
Moisten the cloth and dab at the stain. Do not rub the stain; rather, tamp the cloth up and down on the stain. The idea is to moisten the stain and capture the nail polish on the cloth as it dissolves.
Repeat the process, changing the cloth to a clean spot as necessary as it becomes soiled with the dissolving nail polish. Continue until the cloth comes up clean and the nail polish is removed from the coffee table.