Unfortunately, their docs are explicit about discount codes, "Do not ask the user to perform any other tasks before presenting the payment request. For example, if the user needs to enter a discount code, you must ask for the code before they press the Apple Pay button."
Why? Just make me choose shipping and discount options, then present me payment options. All Apple needs to know is the total to charge. Shopify just fucks this up by only having an option to enter a discount code after you've already missed your change to choose Apple Pay.