Map type. map size and difficulty obviously matter. The issue I had is simply being ahead and everyone ganging up on me in the WC. In fact the only real solution was to wipe out Siam completely so that I got control over the WC.
And let's be honest, what you write isn't possible on higher levels.
Noting that your original issue seemed to be dealing with happiness when conquering with a side comment on tourism i find my comments work on all difficulty levels and while it does generally take longer to get the snowball rolling as you usually need to kill more units to conquer cities, once you start conquering cities it snowballs much easier on higher difficulties as the cities you capture tend to have much more infrastructure already built and are much more developed which generally means less unhappiness generated by those cities when annexed as well as getting much more culture and science which scales with city size with higher levels meaning AI cities are generally bigger.
As vassals provide a percentage of their science, culture, faith and happiness to their master you get much more from vassals on higher levels and vassals become more of an asset against other AI's as they are generally much better able to defend themselves against other AI's on higher difficulties and can even serve as a decent distraction. I usually find the 'harder' part on higher levels is making sure your vassals don't take cities you want as vassals tend to be more capable and agressive.
The AI's tend to have more gold available to buy all the excess strategic and luxury resources you soon have and they can be milked much more easily for gold in peace deals.
Once you reach critical mass the extra AI units are less of an issue and more of a bonus as they are simply extra resources to be farmed as you get culture and science (from authority) and possibly faith when they are killed.
In regards to the WC if you make a concerted effort it is usually reasonably easy to have decent influence in the WC. Focus great diplomats until all emabassies are settled, do city state quests where reasonable and try to build a base of city states (usually close by) that you can control. If an AI appears to be trying to flip one of my city states i tend to park a diplomat next to them so i can flip it back immediately.
Look for 'unloved' city states that are not close to you and propose sphere of influence for yourself on them. It is usually pretty easy to pass this if none of the other AI's particularly want it or there is a more pressing resolution propposed which means you can usually gamble the AI's will deal with the other more important resolutions and you can sneak it passed.
As you mentioned Siam specifically, in pretty much all of my games where SIam was an issue someone proposed the resolution to decolonise them. In fact the AI seem pretty agressive with that resolution in general and even when aiming for a diplomatic victory i tend to try not to claim too many city states until quite late as your pretty much guaranteed to have decolonisation proposed against whoever has a lof of city states.
My annoyance is that you can't really build a somewhat big empire (by just settling, I chose standard Map but reduced number of civs) without everyone ganging up on you and then the neighbor DOWs you, you defend make peace. He DOWs again so you take some cities to put him down a notch and then you are the bad guy? If the same Civ declares war more than once, then taking their cities should not lead to everyone hating you.
Same if the send prophets/missionaries, you ask them to stop, the continue, you denounce, they continue you DOW, then you should get reduced penalites as it's really to a large part the other civs own fault.
For these issues, finding out more about the nuances of the diplomacy system and using the visible diplomacy modifier option can help a lot although generally the more successful you are the more the AI will try to combat you and dislike you. If you make the effort though it is usually possible to keep at least one good friend until the late game although this depends a lot on the civs in the game and who your neighbours are. Sometimes it is simply not possible to make friends and thats part of what makes each game different.
To avoid the spam war situation you have to make yourself not seem like a good target and others seems like a better target.
One of my most memorable 'diplomatic' games i spawned on a continent with the Aztecs and Persia as neighbours and 4 other civs on a huge map.
I avoided war with either the Aztecs until the Industrial era and Persia until the Modern era and was actually 'friendly' with them up to that point amd managed to keep a few other friends until the late game.
I focused on doing CS quests and dropping the odd diplomat as necissary to neighbouring city states so they couldn't be used against me, acted as an additional shield against attack and provided me with additional strategic resources and happiness and when spies became available i put them in further afield city states and managed to grab a couple of those also.
Any time the Aztecs or Persia declared war, apart from against each other i would opportunistically join them once they began to have the advantage and take a city so i was friendly with them from being in a war together and as i only took one city at a time it wouldn't be a huge diplomatic warmonger hit which would quickly dispate with most civs.
I also made sure to focus on my military and rushed the Great Wall as well as making sure to grab any highly defensable tiles so other civs were always an easier target.
The Aztecs eventually DoW'd me the turn the Great Wall expired (the industrial era) which wasn't a surprise so i was prepared and after an intense siege of one of my cities i managed to fight them back and take some of thier cities before eventually vassalising them, making sure to liberate some of the cities they had captured to keep my warmonger hate low with the other civs so i didn't lose any friends.
At this point Persia was no longer friendly with me as i was the only target left on our continent to attack but they seemed reluctant to actually attack me and we traded citadel bombs until i got balistics (modern era) so i could use the additional range and indirect fire before i DoW'd them. I suspect we would have stayed in this stand off for the rest of the game if i hadn't decided to DoW them.
Once i started to take their cites i liberated a few to keep my warmonger score down but as it was now the late game and warmonger hate is quite high and TBH i didn't really care about having friends anymore i just started conquering them until i vassalised them and then it was really just cruising to victory.
