I used to play on Noble, now playing on Monarch with 11 AIs. My usual strategy - refusing demands, DOWing repeatedly - had disastrous results
A lot of good advice so far, but you've already pointed out a big problem. No you don't always need to give into requests/demands, but you must ask yourself what the cost is. If it's an old tech, and extra resource or some gold, it might be worth giving in for the diplo boost or to keep a warmonger off your back. On the other side of the coin, if you already plan to kill that AI anyone, then don't give in. Timing and who that AI is, as well as there proximity to you factor in. Just note that if you refuse a request/demand that AI might go insta-fist mode on you (i.e. start to plot war on you).
11AIs?!! What size map and speed do you play. I might recommend playing normal settings for a while until you get more experience with the game and the diplo side especially. More AIs is just going to make it all more complicated for you. Don't add more AIs than the standard AI allotment for a given map size.
DOWing repeatly? Well, for what purpose. Worker stealing ..yeah sure...but know who you are stealing from and if you steal constantly prepare to take them out later. That AI is dead to you from a diplo standpoint. DOW demerits do not go away. There are some maluses that never go away either like "declared war on friend", so also note who the friends are (well, pleased or better) of the leader you are DoWing repeatly, cause you are getting a hit with them every time as well.
So Diplo takes knowledge of the factors, ofc, but takes planning over the course of the game. Who will you buddy up with - at least temporarily in some games, and who will shun.
There are a lot of Diplo pluses you can get in the game, which many have been mentioned as well. But some take planning and some effort, as they take time to build up. Open Borders with everyone, or at least everyone you plan to keep happy (a bonues builds up over time). You want the trade routes anyway. Trade extra resource immediately when you can for other resources and GPT. Or even gift them for a while. You can renegotiate trades every 10 turns. Heck..I'll even trade or gift single copies of resources - usually health not happy for while too. And if EXP or CHAR you may be able to do without a happy or health for while. Point is to keep the trade going. The trade bonus takes time to build up (to a limit of +2). Note that the more resources you trade the faster the bonus builds up.
Imbalanced tech trades give some fair trade bonus up to +4, or even gift some old useless techs. Bonus goes down over time, but you can trade or gift stuff later to boost it up. Eventually you get bonus for "shared technology" but the amount of techs differs among the AIs..quite substantial. Some as low as 7 or 8 techs, while some as high as 20 I think.
Of course, there is shared religion as well. But keep in mind the folks that are in other religions, and which ones are much more zealous than others, like an Izzy. Generally, you are not going to want to be the only one in a particular religion. You either join a religious bloc, or just not adopt a religion until things pan out.
Lastly, choose your friends and enemies wisely. There really should never be a situation you put yourself in where you are pissing off the entire world. You need friends to trade with and enemies to fight or bribe friends into war. Speaking of which, shared war is another way to build up diplo bonus. And certain leaders you can build it up quite high, although it is a bonus that will decrease with time.
In short, once you have the experience and learning, the diplo situation in the game is something you should control not something that controls you.
even after I changed to his religion, his attitude towards me improved but I am still his worst enemy.
