I had a similar problem the first time that I built a harbor. I assumed that it would show up as a unit to train, but it never did. I tried to design a new one looking for a "boat" option but couldn't. So I assumed it was bugged and gave up on it.
In a recent game I built another harbor and was immediately able to train Transports.
Maybe a save/load would have fixed it? I don't know, but I've definitely had the same issue.