I wanted to win on King with one city and not change governments, so I selected the Greeks since they start with Democracy and that gives you the best science/currency boost. It would make an economic victory the easiest path. I also didn't want to convert any cities because I thought it would go against my "one city" goal. I was able to do this by setting individual hoplites in fortification along chokepoints entering my city, which prohibited others from settling close to me without starting war to get into my territory. I changed them to armies as time allowed. I built up the tech tree without any interference. By limiting my culture and building a wall, the only conversions available were through Great People, and I just didn't allow that. When one civ was getting too strong, I paid off 2 or 3 others to go to war with that civ.
Of course, when the end of the game came, I befriended the only civ who hadn't declared war with me and bought the tech I needed to properly defend my city. Then she immediately declared war aftewards. Good thing I did that because all 4 civs came at me in waves with bombers, tanks, and artillery, but I was able to hold them off with modern infantry armies, upgraded to 120+ defense, which nothing they threw at me dented. After that, I knew I was home free unless they overpowered me with spies, which would have meant I had to stop building the World Bank and switch to some serious spy production to counter. But I didn't have to. Of course, if anybody had the Manhattan Project, it could have been a much different game.
The disappointing thing was that I didn't get the "not changing governments" achievement and I don't know why. I never changed governments and stayed with Democracy from beginning to end. Anybody know why that might be?