Log into your Amazon account and click on the banner that says to save $10 at Amazon for changing your 1-click payment to Discover. YMMV.
This is the link that led me to the offer: http://www.amazon.com/gp/adlp/discover1click
The item must be sold and shipped by Amazon (with exclusions, see below) and redeemed by 11:59 p.m. PT on July 30, 2017.
TERMS AND CONDITIONS
• This promotional offer applies to the purchase of eligible items made with a valid Discover Card. The $10 credit may be redeemed on the purchase of physical products sold and shipped by Amazon.com, and excludes gift cards, Kindle eBooks, instant videos, MP3s, and all other digital content and downloads.
• An Amazon.com account with a valid Discover Card is required to claim and redeem this credit. If, for any reason, your Discover Card is inactive, denied, or ineligible, you will not be eligible to claim or redeem this credit. You are responsible for the final purchase price after the credit is applied, plus applicable taxes and shipping charges.
• Credit must be redeemed by 11:59 p.m. PT on July 30, 2017.
Unredeemed credit will expire after that time. If any of the products purchased with the credit are returned, your refund will equal the amount you paid for the product, subject to applicable refund policies. Credit redeemed on a Kindle or Fire device will be applied to the Amazon.com account registered to the device.
• This promotional offer is valid for a limited time only. Offer limited to one per customer and account. Amazon reserves the right to modify or cancel the offer at any time. If you violate any of these terms, the offer will be invalid, and the credit will not apply. This offer may not be resold, is nontransferable, not redeemable for cash, and is void where prohibited by law and in case of fraud. This offer may not be combined with other offers.
Offer available only to customers who were served an advertisement promoting the offer. To claim the offer, customer must first click through the ad and then complete the additional actions described.