I found this at a website:
How to remove stains on you granite countertops
Do not panic if you stain your granite, because you can easily clean off stains with a few household items. Depending on the kind of stain, you may need to use different mixtures.
If the stain is heavy and cannot be removed by simple warm water and mild dishwashing liquid, then create this sure-fire formula – combine together about one to two tablespoons of dishwashing liquid, one cup of flour, and just enough water until the solution becomes thick (about the same consistency as paste). Simply put this solution right over the stain. Cover the area with a plastic wrap. Leave it overnight. You can then scrape the mixture away gently, preferably using a wooden utensil. Rinse. The stain should be gone.
Oil stains such as grease stain, oil stain, or milk stain requires a different solution altogether. Combine together hydrogen peroxide (in place of dishwashing liquid), a cup of flour, and enough water to make a paste. You also need to put this solution on the stain, cover the area with plastic, and leave for about 12 hours. The stain should be gone when you scrape off the mixture in the morning.; If this does not work, replace the hydrogen peroxide with ammonia.
Is the stain organic (such as tea stains, coffee stains, or fruit stains)? Then you need to combine hydrogen peroxide (about 12% will do) with about two drops of ammonia. This solution should take organic stains off immediately.
If your child left marker stains from working on his artwork right on your countertop, do not worry – you can still remove them. Try either acetone or lacquer thinner – they are great for wiping marker stains off dark granite stones. Is your granite on the lighter shade? Then switch to hydrogen peroxide. If these chemicals do not work, then try a stronger formula – combine pure bleach and molding plaster to make a paste and then spread it over the ink stain (this also works for wine stains). Let it sit for about half an hour, then remove the paste and rinse the area.
They also mention something called " Stone soap" on this website that can be bought at Hardware Stores.