If you have small children, it is likely you have to remove magic marker ink from walls, carpets, and countertops on a regular basis. If your child gets hold of a magic marker and draws on your stone, you will have to remove the ink stain as soon as possible. Otherwise, the ink will soak into the stone and will be much harder to remove. This is especially true of unsealed stone, which has no protective barrier from stains.
If your stone is light colored, dip a toothbrush into hydrogen peroxide. Use acetone if the stone is dark.
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Gently brush the ink stain until you remove it. Work from the outside the marker stain toward the center. Apply as little hydrogen peroxide as possible.
If you can still see the stain and you are cleaning light-colored stone, repeat the process with bleach. If you are cleaning dark stone, use paint thinner.
Immediately rinse the area with water, and dry it completely.