So what was the end result?
I held off Persia, with my city down to 100 health. We went through the peace treaty duration and Persia declared again, this time with corsairs and frigates. I was able to heal my city to 400 health. It didn't stand a chance....
Important note I forgot to mention earlier, I have fealty, so I actually have an extra 5 CS over a normal person.
The other thing to remember is...I am not facing 1 navy....I am commonly facing 5.
Last note is....I did not put this city in a super vulnerable water spot. It can only be hit from 3 water squares with ranged, and only 1 square with melee ships. I have lots of area for my ranged units to fire. God help me if I tried to hold a city with 3 coastal tiles and fewer land spaces that can hold ranged units.
So what is going to happen is, next game I am not going to settle any coasts....I simply cannot defend them, so I'm not going to try. The enemy navy will then have no point.