I think that diplomatic capital is a rather confused concept. The AI respects it, but for no apparent reason aside from it being called 'diplomatic capital.' In my humble opinion, it either needs to be removed from the game, or have a tactical function in the game.
For example, it could have something to do with religion. Create a 'prophet' unit type which cannot attack or defend, but can, if stationed in a city, provide a small boost to prestige for that city, or in times of war, send a prophet to an enemy city to steal part of the enemy city's population, giving it to the city which the prophet came from. Or, even use them to move population between your own cities in the same manner.
Or, it could have something to do with actual relations. Create a 'spy' unit which is invisible whose function is to provide LOS intelligence on enemy troop movements and city information, and to find and take out enemy spies. Arm the spy unit, and get an extremely expensive invisible assassin unit for straggling enemy units or outposts.
Either of these units would require diplomatic capital to make, the same as how iron and crystal are used. Given the resource's rarity, this would make both human and AI opponents actually have a reason to covet this resource. If they don't have any natural sources of their own yet, they would still want the resource to create some defensive spies, to be able to counter enemy spy actions. Or defensive prophets, to counter enemy prophet actions.
