You can find the applied coupons/discounts at the invoice Object level[1]. If there are many, you can expand[2] the discounts field[3].

[1] https://docs.stripe.com/api/invoices/object#invoice_object-discount [2] https://docs.stripe.com/api/expanding_objects [3] https://docs.stripe.com/api/invoices/object#invoice_object-discounts