Sounds very much like what I bought recently to try out. In the camping section of some store (I don't remember which, though) I picked up a waterproof match container. Stainless, rubber O-ring, screws shut. Might be a little longer, maybe 3 or 3.5 inches, but the same diameter. I was going to just cut down a pencil to fit. That and a small roll of paper, maybe preprinted with spaces for date and name.
I also found, in a pet store, these small screw-shut containers meant for attaching to a dog's collar. A tiny slip of paper came with it, for the owner to put their contact info. These are very small, maybe 3/8 inch long, and about 1/4 inch diameter. Have to replace the paper every find or two. Or maybe, just put something in there, and have the finder report via email to verify the find.