No such thing as "possum only" bait. The reason you are catching more oppossums than coons in the cage trap is because coons are smarter and more trap wise.
I had coons eating cat food on my front porch, and they would stay at the back of the trap on the outside and work and work until they had the bait even if they had to turn the trap over and wouldn't go in.
I was watching through the window. The next night, I caught a oppossum in the same trap.
About a week later, there were 2 coons back eating the catfood. This time I just ran out the front door with the .22 and got one. The other escaped in the dark.
About a week after that, another oppossum. The softball bat took care of that one.