Well, the thing that most of Autocracy is about making it very good to fight a war then.
Gunboat Diplomacy is added on top of it, and doesn't really fit well except that if you were planning on fighting you'd want a larger army which is what's needed to intimate the city states.
The best synergy for Autocracy diplomacy is the case of city states had previously been conquered by some other player. In this case, you would be using the military bonuses from Autocracy to help liberate the city state, which instantly makes you allies. If it starts to degrade, just station some troops nearby.
Conquering a major AIs city near a city state is a great way to get a military base close enough to station some troops to intimate the city state.
Related is the Autocracy cultural victory, again the culture victory bonuses are attached to what's mostly making your civ great at conquering. Basically the synergy there is a combo of conquering someone with a bunch of great works to relocate into your empire and also the tourism bonus for shared allies.
Liberty is for self founding a wide empire, Tradition works better if you only found a few cities but use warfare to later attach a wide empire to the tall core. (Monarchy's 50% of pop unhappiness in the capital is much bigger than the happiness bonus from Liberty)