Amazon offers a lot of coupons on diapers of brands like Pampers, Huggies, Eco by Naty and others. They are scattered across various pages on Amazon.com and tough to quickly scan them. Also another type of discounts available on Amazon.com are Open box Deals. Open box diaper deals, not a well known secret, saves any where between 10%-20%.
You can check all coupons as well as open box deals on this website - https://www.babydiaperdeals.com