On the payment page, under the total for your subscription payment, you will see an input box under the words "Coupon code". Input your coupon/discount code into this box and then click on the green "Apply" button. The discount will automatically be applied to your total cost.
Please note: This is not where Paddle asks you if you have a coupon code. If you input the coupon code on the Paddle checkout screen then it will not work.