Update: Looks like the Publix coupon states it is for boxes 15.6 oz or larger which I misread. Sorry.
You should be able to score 4 free boxes of Cheerios this week at Publix. On the back page of their weekly sales flyer which you can see online here, they have 8.9oz boxes of Cheerios on sale for $1.99 each (limit 4). Print out one $2 off coupon per box of Cheerios from their Great Deals on Great Meals site which should make each box free. Even better, pair the deal with some manufacturer coupons and you can tun it into a money-maker.