When I was in the business I was not a fan of coupons…And being removed from the business so long, I can not not comment on what works best these days…
But, my experience was that if we kept sending out menus we kept our sales moving…But one needs to calculate whether spending more money to increase sales was more profitable than using coupons which often increased sales but also food costs…In my method we increased our marketing costs but it gave us a better return than coupons…
It is possible to put a menu in each home every 4 to 6 weeks with a feature pizza and/or product that may pull more than some sort of discount coupon…This depends on your market and you must track everything you do…Excel should be your best friend…