We warmongers have it tough.
I've found that rivals will tolerate war, but not utter extermination. As long as you leave your targets with at least one city, you stand a chance of keeping a trading partner or two.
As for happiness, make sure you keep only the best cities. And target rivals that have luxury resources you do not.
Finally, ensure you can defend what you take and pick your first target wisely. I always go for a neighbor with good land and fewer friends, even if they are more advanced. Keep in mind that the AI has terrible tactics, allowing you to prevail in the face of better and more plentiful units.
Brave New World
This expansion changes the warmonger diplomacy penalty mechanics considerably.
- Smaller penalty for declaring war. While tricking the AI into declaring war will still save you from this penalty, the penalty itself has been lowered.
- No extra penalty for eliminating your target according to this Reddit discussion.
- Per-city penalty for taking each city that scales based on the number of cities the rival has and the map size. Taking a city from a small civ has a larger penalty than from a larger one. This penalty was halved for other AIs at war with your target in the Fall Patch released on October 15th, 2013.
- No penalty for retaking a city that you settled.
- Liberating cities reduces the warmonger penalty.
Halcyan2 started a warmonger strategy thread on CivFanatics that discusses many of these.