Your god may give you useful non-artifact items as sacrifice gifts, such as a stethoscope or bag of holding, so long as you aren’t carrying one of them already.

A slightly more advanced system that wouldn’t require carrying a bunch of items to avoid getting duplicates would be to track the last time you picked up or put down each type of object, and if you have never touched one or it’s been a sufficiently long time, you are eligible to get that item as a gift.