While coupons, promo codes, etc. cannot be automatically applied during online registration, you can utilize a few Jackrabbit features to get the job done!
Add Coupons/Codes to Online Web Registration
Go to Tools menu > Edit Settings > User-defined Fields, label a Family User-Defined field as "Enter Coupon#". This will provide a text box on the Registration Form where the customer can enter the information.
Post a Credit for the Promotion
Go to All Families (menu) and use the Family User-Defined Fields filter to identify the families that need to have a coupon credit posted to their account. Follow the procedures outlined in Post a Credit - Groupon Credit Example to apply the credit to the account.