I just leave them be, sickness is not a threat to my city, and unhappiness is a somewhat greater, but still not dangerous, threat to cities. However, I don't like to waste, so I prefer to let my cities grow however the governor wishes. The only times I even enter the city screen are to change specialists, check GPP's, and occasionally to change the tiles harvested (the governor can be a bit illogical, choosing a hill with one hammer and one food over a plains w/ farm with one hammer and two food, for example.)
I always settle their cities by resources, not really for the resource benefit, but for the tile yeild benefit. I am guessing this is not a rare strategy... I love it when I spawn by about 4 or 5 seafood tiles; my capitol grows insanely fast, and it helps pump out settlers. When I get those kinds of games, I usually win.
Actually, something I just thought of, a very abstract use for that "no growth" button would be if you had a city that had massive amounts of food, and low hammers, and you wanted to produce settlers, you could use that button to keep the Pop. low, maybe for just one turn, thus having more production for workers. IDK, sounds like it wouldn't work though, just a theory.
Aaaaand... I'm rambling.