So I thought a rivet might be the answer.
I didn't like the way the edges were so uneven. I tried using different scissors to add detail to the rings and tried using rivets. This did not go well either.
Then I tried using a wire and rolling the edge around the wire. But the rivets didn't seem to work with this.
So finally I thought wrapping a belt around the middle right be the answer: I could rivet around the center and where the two pieces of metal overlapped. Yes, this was definitely better. I made them from a vintage 1950's tin doll house.