If the AI sees you as weak it will DOW you simply because it thinks it can walk all over you so having a good military help to prevent DOW's from happening
There is a proverb from Sun Tzu's Art of War: "Appear weak when you are strong; strong when you are weak." IMHO that holds especially true here.
I want the DOW. What I do is intentionally have a weak military so as to draw the DOW. But not so weak that I will get trounced on. War is good. It gets your units experience, it gets you great generals, it lets you pillage and steal workers from him. If you get him to DOW on you, it is he who takes the diplo hit--not you. All you have to do is never settle for peace until he is on his knees begging for it.
Three tricks I do to appear weaker than I really am:
- Partially train military units, but don't complete them. Saves on maintenance and unit supply.
- Relocate them to city-states to protect their borders against barbs. Get some free influence from them while you're there. Just picking off one barb in/on a CS's borders, and you earn yourself 12 more turns that CS will be friends with you.
- Corollary: become friends with a militaristic CS or two. They start gifting you with units--which you can turn around and protect their borders with...which makes you better friends....
- Relocate your units on the opposite side of your empire and deny Open Borders treaties, so as to make sure they're never seen.
Once I'm at war, I simply keep picking off his units, pillaging tiles. Pretty soon, *HE* is the weak kid on the block. Guess who gets gang-banged by the other kids then. Indeed it's the AI's who are at peace with you whom are the biggest threat--not the one(s) you are at war with. Never settle for peace unless he's about to nail you or he offers you a sweetheart deal. Once I had the #1 civ (Persia) declare war on me, and I just kept picking off his units and refusing peace treaties over and over again until eventually Persia offered me 5 cities for peace. I struggled with -10 unhappiness, but that pretty much doubled my empire. Couldn't refuse that one. I don't even settle for peace when the AI's down to one city (and not his capital). There's nothing in it for me. I let some other civ take him out for good, and he takes the diplo hit instead of me.
The other reason I refuse peace: later in the game I will be friends with a number of militaristic city-states, and all the units they gift start to burn a hole in my pocket. If there's a civ I'm already at war with, it makes it easy to put those units to good use without having to DOW somebody and make everyone else hate me. Especially if that civ happens to have some nice juicy resources I don't particularly care to trade for.