Shopify doesn't have an API to verify discount, however I have found a little work-around.
By making an AJAX call to
/discount/(code), Shopify will set a cookie telling the checkout to auto-apply a discount on visit to the checkout page.
Next, making an AJAX call to
/checkout, we're able to parse the HTML and determine if the discount code worked!
Here's an example of it in action:
For source code of this script, please see this repository.