In order to have access to online coupons for your store club cards, you must first select a coupon provider source, such as Cellfire. This is done in the Settings app.

Tap the Coupon Provider line and tap on the desired provider (at present, Cellfire is the only coupon provider supported):

When a coupon provider is specified the coupon button becomes visible at the bottom of the Shopping List page as well as in the Details page of an item: