To create a coupon for use only by first-time customers, create a new customer type called "New Customer" and make New Customer the default customer type (Customers / Types, p2).
Then, when creating your coupon, be sure to:
*set usability for the coupon to only the "New Customer" customer type (Coupons / New / Usability).
* set the coupon to be usable only one time per customer (Coupons / New / Customer Usage Limit), and
*set up a customer type upgrade on that coupon (Coupons / New / Customer Type Upgrade) so that when a customer uses the coupon they will be changed to customer type "New Customer" , and
This is recommended ONLY if you do not otherwise utilize customer types for experiential differentiation by customer type, such as for pricing, product visibility, club membership, taxability, shipping methods, etc.
Be sure to turn on customer type history tracking if you create this type of coupon.