I consider myself a peacefull/builder player. Not so much because I can't war but because I like to finish my games quick and the peaceful/tech way is just fastest in term of game time.
I'd say good diplo adds a lot to your winning chances. In a lot of my games I don't even need an army in modern age. Who needs armies if you can just dictate what the AI's are doing. Even if I go to war, I don't need a large army usually. Bribe my allies into a dogpile on my target, let them waste sod's and then I snatch weak defended cities. You know these AI's with a power rating that is through the roof? I like them v much.

Though I keep them bussy, bribing them into wars a lot. Being backstabbed is not pleasant.
Maybe some obvious tips:
- Try to decide on a diplo plan early in game already. I prefer allying aggressive AI's because they are easy to manipulate and the pay off can be great. Though they are usually more demanding. Still due their large armies, their tech speed is lower thus on higher difficulty I find them good to trade with. (what use is MM as an ally if you hardly have any techs on him)
- Make a long term diplo plan. Decide on what civs you plan to conquer throughout the game and try to find the AI's that will give you most benefit in the long run. Being able to 2v1 or 3v1 makes things a lot easier. Geography matters a lot.
- Help your allies, they help you. Don't be scared to give them good deals in tech trades. The more advanced they are, the better their military thus the more helpful they will be when it comes to war.
Same goes for demands, just give them w/e they want. (unless it's something really ridiculous)
- Don't try to get any -diplo. "-4 you traded with our worst enemies" is not something you want to see on your ally. Be aware of the diplomacy of all civs towards each other.
If you do have to declare war on an ai they're pleased with, make sure you can wipe them out with one declaration. Or even better try to get them out of pleased mode. (Bribe to stop trading, civics, convert, whatever is available)
I think diplomacy is a big part of the game. And imho good diplomacy requires as much thinking and planning as any other aspect.
And of course in some games you will just have a hard time diplomacy wise. It depends on the map as well. For example I find continents/fractal not challenging at all because diplo is too easy. A few games back I had a peaceful win on fractal without building any military. I'm talking about macemen being the most advanced unit I owned while launching my ship. Hence I like to play on landmasses to make it interesting.