Once you learn how the system works, it's pretty easy to tell when a Civ is going to collapse. If you don't want a Civ to collapse, don't take their capitol. Kill as much of their army as possible, and threaten their most valuable cities with your armies (without capturing them all). The more defenseless (having few units but big cities) you make an AI feel, the quicker he'll capitulate. If you take his capitol or focus on grabbing land instead of killing his armies, you're attacking Stability more than Power, and he'll probably collapse before he feels weak enough to capitulate.
If a capitulated enemy is unstable from the war, gift him back some of the land you took, and perhaps some resources and tech (but land is a quicker fix) to help him regain his balance. Vassals lack the means to improve their stability easily, so you have to help them.
The biggest problem with Stability IMO is that it's poorly documented and has poor feedback to the player... the addition of mouse-over help on the financial screen (like the financial data there has) that gave a more detailed breakdown of what is giving/removing points would make Stability infinitely more user-friendly.
) and I STILL don't know how it works. I've gotten a rough feel for it so I can avoid problems and take advantage of enemy instability, but it still feels extremely vague and grey.
