As far as we know, Happiness is not tracked at all locally. There's no indicator for it on the city screen, only the global indicator on the top bar of the main screen.
To quote your site:
"Legalism: Reduces unhappiness from population in the Capital by 50%?"
So if you have a SP that reduces unhapiness in a specific city, why not a building that does the same?
But I still doubt this will be the case. It would be so much more difficult to keep track of the happy-status since the cities again would need to be treated individually. An exception to the capital is easier to live with. Having to check the buildings in a city to see how growth will affect happiness seems tedious.