1822, "certificate of interest due on a bond" (a piece which could be cut from the bond and presented for payment), from French coupon, literally "piece cut off," from couper "to cut," from coup "a blow" (see coup). Meaning widened to "discount ticket" 1860s by British travel agent Thomas Cook. The specific advertising sense "ticket or document that can be redeemed for a financial discount or rebate when purchasing a product" is by 1906.
COUPON. A financial term, which, together with the practice, is borrowed from France. In the United States, the certificates of State stocks drawing interest are accompanied by coupons, which are small tickets attached to the certificates. At each term when the interest falls due, one of these coupons is cut off (whence the name); and this being presented to the State treasurer or to a bank designated by him, entitles the holder to receive the interest. [Bartlett]