How do I show a coupon code to customers? I've enabled a Ubercart Discount Coupons module in my eshop site and created some coupons with multiple one-time use only codes for testing purposes.

Now I would like to get one of the active coupon codes to customer who submits a newsletter registration form. Are there any functions to retrieve one of unused coupon codes?
The UC coupon module doesn't have a general purpose coupon retrieval function. 

If you're solely looking to retrieve an active coupon, you can follow what the module itself does: query the DB table uc_coupons for rows with column status = 1. Using a DB query will let you modify it to whatever your particular case (e.g. 1 or more results, bulk codes, date range, etc.).