Sean,
It is just pure luck, with the percentage chance for success determined in part by the people´s satisfaction rating. The premise is that content people are less likely to go for it.
This unfortunately is another area of the game that was given a ´lick and a promise´ when they designed it. There are so many levels where they could improve it and make it a proper part of the game. Ever since there was a Royal Court, there have been spies in use. So to have it where there are no ways to modify the chances for success and having 3 options with increasing costs for diminished chances of success is a joke.
A simple system of being able to pick a city, and bribe a local official or two, or even just to place a watcher or two who could report on building queues or troop movements would make a huge difference. At a more advanced level, agents should be able to forment rebellions, disrupt production, steal plans, etc... much like in Alpha Centauri. And it should not be too hard to code either. Most of the basics needed are already in the game.
I´m hoping that Civ IV will have features like that since they were incorporated into other games like Civ II and CTP2. In the meanwhile, indirect methods are all we have like parking transports off the coast out of cannon range and watch what rolls by...
D.