HAHAHA! Someone try Conquest Victory in an OCC! See how long you survive!!!
On chieftain level, on a small sized map, it's very doable. On a huge map and/or higher difficulty levels, yes it would be very difficult.
But actually now that I think of it, that still doesnt tell me exactly what you need to have done during the game to win by Diplo Victory...
Best Reputation is the best answer. You can war, but it really helps if you have allies, and war with the civ that seems to be causing problems on everyone else (the bully). MPP's help get other civs on your side. Trade with civs often. If some civs are at war and you are not involved in the war, watch who you trade with. Even though you aren't militarily involved, you would be treated as if you are supporting the civ you trade with. In one game I had both Egypt and Germany attack Greece. Both were polite or Gracious with me. However, later on Egypt and Germany waged war on each other. And since I was trading luxuries with Germany, Cleo wasn't too happy with me.
If there is some civ that is way behind in tech and doesn't have anything of value to give you, donate him techs, that will certainly help you get that civs vote.
NEVER raze any cities! You don't necessarily lose votes of other civs, but of the civ whose city you razed, you will never get their vote.
If in the modern era, if some civ doesn't have horses or iron (useless at this point of the game) donate them.
Just before the vote donate techs/luxuries to all civs (especially the civs that may be undecided on who to vote for).