@UnicornEmily Carmine (aka Tillamook) is a good option. I do not recall seeing any thorns on my Tillamook and it has good/medium sized goumi with good production. If you want no thorns and good size that is a solid choice. Some of the less common ones likely also meet those criteria but I do not have experience with them to say for sure (Pippi for example).
I also have Sweet Scarlet and Red Gem. In my experience, Sweet Scarlet and Red Gem do have what could be considered thorns that are like short branches. Linked below is another thread on goumi where there is a picture that is probably either Sweet Scarlet or Red Gem and you can see what I am thinking of in terms of those two having thorns.