Why even make them go to Google? Put a link right next to the coupon code: Don't have a code? Take our <a href="#">3 question survey</a> and get one now!
Then you can learn a bit more about your customers, and make them happier about buying at the same time.
Or just ask the customer to subscribe to your mailing list to receive coupons. You can send them one coupon immediately for their current purchase (possibly even applicable retroactively if email is slow when they are completing their purchase). Then you can send them more email coupons (and personalized recommendations) in the future to keep them coming back. :)
Then you can learn a bit more about your customers, and make them happier about buying at the same time.