Go here (media.ajc.com) to the AJC website and click on "Subscription offer and coupon" in the right hand corner. It should print a coupon for $1.00 off the Sunday paper - the coupon is good ONLY on SUNDAY.
The coupon states to use it at Kroger, but since Publix takes competitor coupons you should be able to use it at Publix as well. From what I understand you can use the coupon on a single paper or a double pack of papers. The coupon reloads every week so each Sunday you can print a coupon to use on your paper that week.