What triggers "We love the King (or whatever) day?" I can't find it in Civipedia.
I think it is available to occur when you have
"
Cities of size 8 and higher which have no unhappy citizens and no food loss to health can enter "We Love the King Day!" from time to time. The effect is that the city pays no maintenance for one turn.
Each city that is eligible has a random chance to celebrate on any given turn that it remains eligible.
So if you have size 8 city (or greater) and there is no sickly green face icon nor a red angry face icon next to the city on the map screen, it is eligible.