A customer coupon guarantees that a customer will come into the restaurant at tomorrow or at the day after tomorrow. They first appeared in Papa's Sushiria. They were introduced so the player can complete certain Stickers faster (such as serving a special to a certain customer or putting a certain ingredient or ingredients on a certain customer's order).
From the Flipline Studios Blog
This week we wanted to introduce you to a customer who will be making his debut in Papa's Sushiria, Vincent!
Vincent is a traveling mailman who loves to stop by for a quick Sushi fix. He's not only here to eat, Vincent's here to help too!
When we introduced stickers in Papa's Bakeria, we made several quests where you had to serve a specific customer specific things. Unfortunately, this could sometimes take a very very long time. See, if you had to serve Rico a specific Special, you would have no idea how long it would take before Rico returned. Sometimes you would be waiting months before Rico would stop by the shop again.
So we solved that problem by creating Customer Coupons that you can buy in the shop.
Once you purchase a Customer Coupon, you can send it to anyone of your unlocked customers.
Once sent, Vincent will head over to that customer's home to deliver the coupon.
After that, you will be certain to see that customer return by the next day!
Vincent will also be taking over the job of delivering new outfits to customers! 
How it works
The player can buy customer coupons from the upgrades section of the shop for $25. The player is allowed to have more than one on hand, but the player can only deliver one per day. To deliver a coupon, the player must go to a customer's profile and click on the mail icon on the top right. It will show Vincent delivering the coupon to the customer outside their home or apartment suite. The player cannot deliver coupons to Closers, as the button will not appear in their portrait.
- If delivering a coupon to Vincent, Akari will give the coupon to him.
- If the person delivering is in their Style B outfit or any other outfit, they will deliver in said outfit.