I use their papa johns codes frequently, they always seem to be good for 40% off - however lately I've noticed papa johns trying to cut out the middleman and run their own coupon adwords offers
Papa Johns is partnered with MLB again this year. If a team scores 6 or more, your online order the next day is 50% off. I'm not sure if you have to be local or within a certain mileage of the ballpark. The promo code is usually yankees6, mets6, rays6, etc, as you can see in their NY twitter account below.
They also have an affiliation with the New York Rangers for 50% off the day after the Rangers score 3 goals. It's amusing to me how aggressively they advertise in NYC when all the alternative pizza is cheaper and better.
I think what I was getting at is that there are no chains that compare to the small pizza businesses in NYC. I prefer Domino's to Papa John's if we're comparing chains though.
https://twitter.com/PapaJohns_NY