Means you’ve been warmongering for too How do I make friends in Civ 5? Although this is Civ 4 and not 5, it’s likely that the AI “cheats” in the same way in Civ 5, so even if you’re playing on Prince, the rules aren’t exactly the same for you as for an AI. The difficulty bonuses for the AI is probably not the only way it “cheats”. The AI normally sniffs out this opportunity to claim a city very quickly and gets straight to work on it, so you’ll need to act fast. To convert a Free City to your Civ you can do two things – increase Loyalty pressure on it from your Civ, until it swings into your control, or conquer it with military force.
Elizabeth's ships of the line are perfect for this duty. Once you have it, you get the surrounding ocean as safe harbor where any unit of yours can heal and boats can easily move in and out of mainland city range. If you have a naval advantage, the IC can easily be bombarded so that just about any embarked unit can take it. I love one tile island cities to set up for assaults on the mainland.