I can make a new discount but I can't get it to let me make a promo code for my website.
Hi there.
You'll need to toggle on the option to "Make this discount available in your Online Store" to allow it to be applied as a promo code.
You can read more on how to do this here.
The option "Make this discount available in your Online Store" is no longer available when I create a discount. Am I missing something? I used them in the past, but can't seem to figure out if there is a new way of doing this, or if discount codes have gone away for some reason.
@tcphoto - You'll have to navigate to a location specific dashboard before you'll see this option. Just click on an item, select a location, and then press go. Here is a screenshot:

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