Absolute black shouldn't stain and shouldn't need to be sealed. It's possible that your granite was sealed and the stains are showing up in the sealer. In that case you need to remove the sealer. Alternatively, you might not have been sold authentic absolute black. You should contact your fabricator.

Weissman,
Yes the countertop was sealed; I remember the installers applying the sealer. I didn't know that it shouldn't be. How would the sealer be removed?
Thanks!

I agree with Weissman. Absolute Black is the most dense countertop granite. Consequently, it should not be sealed because the sealer cannot penetrate the granite, and then sits on top of the stone creating a haze, and showing water marks and the like.

I am linking a recent thread, and also you could go on the John Bridge Tile and Stone Forum and ask the experts there with a post liked "How do I remove sealer on Absolute Black" or something like that. They are very friendly there to the "non-pro's", and you will get advice from guys in the business (without having to pay someone!).

Here is a link that might be useful: Kitchens Forum Thread about AB Sealer

Use Silestone Iconic Black! I bought this and used it! It perfect with no problems!