Improving pigmentation is a gradual process. You should start to notice some changes within a couple weeks, but the progress is incremental.
For pigmentation problems I would recommend the Lactic 50% Acid peel or the Glycolac/60 Acid. Both of these Skin Laboratory products are safe for use on dark skin, and are effective against hyperpigmentation. The Glycolac/60 also contains Glycolic acid which helps to stimulate collagen in the epidermis causing a reduction in lines and fuller skin. By getting the combination you can get both in one treatment.
When you first start, apply it to a test area for 1 minute and then rinse off. Wait 24 hours, and if no problems you can apply the peel. I would apply once a week at first, and adjust according to your individual skin sensitivity.
For oily/acne prone skin, alternating between lactic and salicylic peels provides very good results, and is not as harsh as salicylic or glycolic alone. If alternating, apply them 3-4 days apart.