Seem to have NO naval options

I am running as Boudicca, King, Continents Plus, Quick and Large.

To my North I have Sweden; to my South I have the Zulus; to my South-East I have the Shoshone; and to the East I have Russia, Aztec and Germany. I have not found any city states yet.

I am in the middle of the continent and had just found a good location for a naval city. The Zulu had one city 7 cells to their north, about 11 cells away from me. Both of those are on the sea.

Suddenly, over about 5 turns, he created 3 cities - one 5 cells to my South; one 7 cells to my East, where I would have put a city; and one 5 cells to my North-East. I managed to create a settler and create a new city to my North-West, expecting an attack from Zulu. Instead, Sweden asked my to join him in a war against the Zulu, since the last of his cities was getting near to Swedish lands.

I agreed, after a 10 turn delay. Over about 30 turns, I managed to take over all 3 of the Zulu cities. I razed the one to the South, annexed the one on the coast and pupetted the last one. It seems that they got no military support from their capital.

Sweden seems not to have actually joined in the war, though I did see a Zulu warrior that was damaged, and a Swedish spearman to my South. They are still actually at war.

Having built the courthouse in the naval city, which I have renamed, and completed Sailing and Optics, I have just released that the city has no naval options - no trireme, no work boat, no cargo ship etc.

Is this because it is an annexed city, and do I need to build another city to get the naval options?

annexed city with a courthouse should be treated the same as any city you founded. A screenshot would be super helpful, as would posting a save game file, so people can take a look at the situation and try to figure it out.

Any chance it is just on a lake instead of the ocean? I built two cities on a giant lake (25+ squares) and am now hating myself for it.

Yea I would suspect you didn't notice and that it is actually a giant lake rather than an ocean

Although it is also possible to have naval units within a lake, you have to also have it connected to the ocean*

Or is it possible it's not right on the coast, but maybe a tile inland?

Firstly, it is a small lake, having just walked around it. Secondly, I have created a new city on the lake, and that one does not get the naval options. Thirdly, I have created a new city on the coast, and that one does get the naval options.

I wonder if the issue is that you only get the naval options if you are on a sea, defined by have ocean cells and not just coastal cells.

But in my last game, I found a single cell lake, in a desert next to a razed Carthaginian city not on the coast, which had a quinquereme in it.

And just make things worse - Gustav has created a city north-west of my capital and south-west of his. No issue about that, but then he declares peace with Shaka and GIVES HIM the new city.

My guess is that the land between Shaka's capital and me is jungle, and that Shaka is looking for plains and therefore jumps over the jungle cells. Sooner or later, I will have to remove him.

You definitely should try to post a screenshot.