Since people have been pulling them from circulation, they might be more rare than the zinc ones, but they do turn up. When I go through my pocket change, I weigh the 1982 cents and I do find a copper one occasionally. I think I found one this past week (and I don't get lots of change during the week).
The only variety that is rare is the Denver Small Date Copper. Only one has been discovered, so I continue to doubt its legitimate existence. The rest can be found with only a little patience. I'm not even a cent collector and I have extras.
In Memory Of Tootallious 3-31-1964 to 4-15-2020 "Riders in the Sky"