Acanya Coupons and Discounts. Acanya is a topical medication containing benzoyl peroxide and an antibiotic called clindamycin. The price of Acanya is typically around $500 and can cost over $600 for one gel pump.This medication can be difficult to afford without adequate insurance coverage. If you’re having trouble affording this medication, take advantage of our Acanya coupons to cut the cost by as much as 75%.escription: We keep track of all kinds of deals from drug manufacturers and provide links to them on our site for our visitors. The Acanya manufacturer is currently offering a savings card that can reduce your copay to as little as $35 if you have insurance and as little as $75 if you pay in cash.