If you're looking for a renewal and a promo code, you probably already know that they only work on new registrations or products.
By luck, I was able to 20% off by:
1. Going into the Manage My Domains list and enter the Domain Settings of the domain you're looking to renew. MAKE SURE your cart is empty otherwise the last step will generate an error.
2. Scroll to the bottom of the page under Additional Settings, you'll see a link to "Transfer domain away from GoDaddy", click that
3. Complete the form, put anything you want or nothing, then submit
4. You should see a page that says "Here's 20% Savings On The Line
When you renew with us for 1 year.
(And stick with the industry leader.)", see attachment
5. Click accept offer and the 20% off will appear in your cart not as a promo code, but simply taken off the renewal base price. Even though it says 1 year only, I was able to renew at $11.99 for three years, not the BEST price but competitive enough for me to not worry about