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.
“Many people prefer lactic acid because it is gentler on the skin, especially if you have dry skin.
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.