Options to take over an AI controlled city?

No, there's no cultural conversion of cities in Civ5. Even the options for taking owned tiles have been limited somewhat.

It's a terrible position for them to be in though - if they're surrounded by your boundaries, there's no way to expand their own. Buy up whatever tiles you can to surround them, and then try to cut a deal to take over control of the city. Usually the AI resists trades that involve cities, but they will sometimes place low value on really poorly located cities.

If it comes to war, you'll be at a significant advantage, since you'll essentially be cutting their supply lines and surrounding them with hostile units with the "friendly territory" bonuses (if you have them).