After the coupon code is entered and the discount is applied the cart displays the discount amount on the confirmation page and confirmation emails not the coupon code entered. The coupon code is displayed in the manage orders screeen accessed from the store admin menu so you can see the coupon entered with the order. Also, the coupon entered is also stored in the orders table in the database. Currently, there is no coupon token that you can use to add the coupon code to the email.
-Scott