Try deleting the cache and moduserdata folders at \Documents\My Games\Sid Meier's Civilization 5\. From your previous saves, your games are not calculating the unhappiness of your empire correctly, since that is the value that spikes up after you load your save (as opposed to your happiness sources dropping).
I suspect this has to do with the auto annexing bug I posted earlier in this thread. So save and load each time you take a city so the game has a chance to recalculate your happiness values and you don't keep getting blindsided. And note how much happiness and unhappiness your empire is generating before and after the save/load.
Frustratingly enough, I can't reproduce this bug even in my warmongering games.