Why is the New coupon button greyed out on my Coupons page?

Depending on your plan, the Coupons plugin allows a set number of live (active) coupons. The count shows next to the heading on Marketing → Coupons, for example "5 of 5 live", and the + New coupon button is disabled once you reach it.

You have two ways out:

1. Edit an old coupon and untick Active to free a slot. Inactive coupons don't count.
2. Buy more under Coupon capacity at the bottom of the same page.