Same for me. I play both in AM and PM and have never seen more than one. I do see them on mystery islands sometimes.In my experience so far, I only get one message in a bottle on my island's beach in the AM. I get none during the PM. I would collect sea shells during the PM time and never saw a message in a bottle--not even once. If I go on mystery island tours however, I sometimes find a message in a bottle on the beach too regardless of it being AM or PM as it appears randomly.
I get between 1 to 2 with each human used on a given day.
This is more common if I have a human play at different points in the day.