I recently won a OCC on monarch.
The trick is basically not to be attacked. To archieve this you'll have to trade alot with the AI and give them a reason not to attack you. Atleast in my game I almost managed to do this, although I was almost wiped out in the ancient age.
Since you don't have much land or resources, the AI doesn't seem to interested in attacking you, and with the help of Right of Passage and other deals you might make it.
Since you only have one city, a 20k cultural win was, atleast on monarch, quite easy. Your city will soon be the biggest in the world and can produce wonders faster than other cities. All you need, is to keep up in the tech-race. The great library can become very important here, and later Copernicus and Newtons Univerity helped me to research at an acceptable level.
On higher difficulties keeping up in tech will be tougher, so diplomacy might be easier. But you need to build the UN yourself to get in the election, which might be very hard.
An OCC is a very different and interesting game, and it is also quite fast. You should give it a try. It really helps out your diplomatic skills.