Radio Station Happiness
I could be wrong, but I'm under the impression that the happiness boost from the radio station is a passive benefit, rather than gained upon activation. I've been ignoring the fully-staffed (max charisma) triple room radio in my vault because I don't want new dwellers right now, and my population is sitting at around 91% happiness. I haven't started to manage my dwellers to improve happiness (e.g. by having low-happiness dwellers start families) beyond putting both males and females working together in each room.