Currently, there isn't a way to add the coupon codes in the cart page to preview what their checkout total would like. The very first screen after your customers click the Checkout button on the cart page will let them input their discount code though, and update the order total.
However, a discount estimator tool for the cart page would be awesome and I would be happy to share it with our team as a feature request :)
Have a great day!
You can add coupon field on cart page, or cart drawer.
This app works perfectly for us: https://apps.shopify.com/discount-coupon-field-in-cart-page
See it here:
I see that you have already found a solution for showing Apply coupon field on the cart page.
However, we have recently launched Voila - Power Coupons on Cart with which you can also show selected coupons on your cart page.
Showing the right coupon codes is a proven way to boost Conversion Rate & AOV.
Let me know if you have any questions or feedback.