Update 7/21/2019: Both codes below are dead...
My UPS premium service would be expired today, and I found that the following two coupons were still good (tested on 5/20/2017). I used $10 coupon for renew, but it should work for new account as well.
BZTTLG7D7 $10 for 6 months (from upsmychoicedeals.com) (Dead)
BTH5ZYHD3 $3 for 3 months (from slickdeal post
DONT FORGET TO CANCEL AUTO RENEW
I tried these coupon on UPS website, but all the coupons (no matter expired or not) were shown as "Missing or Invalid RequestType ". Then I tried the iOS app, it worked there.