That's the holy grail of the star sprockets, the reflectorized one. Someone here was trying to follow the serial numbers of those Arkansas made AMF bikes, but hadn't been able to find a sequence. I had a frame with the same sprocket, the serial started with a P. It's on the left dropout I believe. I would guess late 50's early 60's, I think they went with the next version of sprocket by 1965, I'm not sure of that though. Does the seat stem tighten like a handlebar stem (wedge) or does that collar tighten it? That would make it early 60's and before if it's the style with the wedge.
Anyway, it's in good shape and a decent bike. It looks like the rims were changed out, if it was a rental at Put-in-Bay, probably. They probably used heavy duty rims as replacement wheels, it looks like a red band Bendix coaster so it wasn't a recent change.
I remember riding the crap out of the tandem rentals at Kelley's Island as a kid.
