This statement appears on the FAQ page at booking.com…
Does Booking.com offer any special consideration discounts, or discounts with airline or hotel loyalty cards?
Booking.com provides the best available rates for the dates of your stay. It is not possible to have any further reductions on the price.
Can I use discount coupons (e.g. issued by magazines, stores, etc.)?
No, you cannot use discount coupons when booking on our website. In such cases you will need to follow the instructions given by the organization issuing the coupon.
In other words, you cannot use a coupon code of any sort on booking.com. If you are in possession of a discount coupon that claims it’s valid for booking.com, follow the instructions laid out by the organization that issued the coupon. Those instructions may include phoning a certain number or accessing a specific website other than booking.com.