I'm looking forward to when someone smarter than myself tears the code apart, and we all discover the war weariness mechanics.
For now, I have been able to get myself a net gain in effective amenities through war, even without capturing any cities. If you pillage every upgraded tile your opponent owns except the luxury resources, you will find yourself swimming in resources, and they will give you the luxuries when they sue for peace. The final blow is usually to the capital, and I accept whatever cities lie between my civ and the capital I'm taking in the peace deal. The capitals are almost always worth any warmongering penalties I take along the way.
Most important:
Create a line of defense as soon as a leader DOWs you. You don't want them pillaging your tiles.
Don't lose units. Ever. You can almost always get the strategic upper hand over the AI. In multiplayer, a long war is a bad thing for both sides, so a small gain (even one lux or a few gold per turn) is worth the trouble to keep from falling behind the rest of the players if you can't overwhelm them without losing units.
Kill off your opponent's units quickly, then go and pillage.
Pillage, Pillage, Pillage, but don't pillage luxuries.
If you want their capital, go and get it. Don't take every city along the way. Take the capital, then ask for other cities in a peace deal.
If you are going to take a city, don't pillage their districts. It takes forever to regain that production.
If you keep those wars quick and decisive, and also pillage the opponent's infrastructure along the way, you can make sure that their growth is stunted enough, that you can basically farm them for resources, and goad them into DOWing you, so you can repeat the process at will.