A friend of mine used to have dark underarms as well. If I'm not mistaken it was because of the deodorant that she was using and her frequent shaving. Her mom noticed this and she (her mom) advised her to apply lemon juice and honey in her armpits before taking a bath. Her mom also purchased a topical treatment called Whiterderm that she applied everyday in her underarms. I think it worked well for her because she can now wear sleeveless tops.