It's simple, As per my understanding, you want to send the email with discount coupon automatic to your new subscribers. Is that right?
Your Confirmation email template
You can include the discount coupon in your confirmation email template. The email will send automatically whenever a new users sign up for the newsletter. Go to the Settings > Notification and edit the following template.
I hope it solves your issue. If you still facing issues, let me know. I will help you out
I have given the solution above. Still, if you are facing problem. You can reach out to me:)