[jandrese]

Diplomacy isn't about sucking up to your rivals, it's about making invasion too expensive for them. A big military is a diplomatic asset. Nobody wants to pick a fight with the guy who is going to kick their butt. A tech lead is another diplomatic asset, although one the Civ AI is kind of bad at recognizing. Swarms of pikemen against artillery and machine guns is not a good strategy. Having a lot of friends can also help, but in a fight they usually won't stick their neck out to help you, even if they're always begging for you to go to war against their enemies.

Downside of Civ V is that the AI is just not up to the task of waging war. It's pretty typical that they'll have 4-5x as much army when they declare war and you'll still wipe them out without a single loss. Between the fairly tanky cities, easily abusable terrain, and general AI incompetence there is a lot you can do to bleed an enemy dry over the course of a few turns.

But of course after you've killed one Civ, even the one everybody hated, they'll call you a Warmonger and constantly denounce you. At least your city states will still love you, especially if you've gone for Freedom.