The Tholos of Idols is provided in this event. It has a big happiness boost for low-aged players. Combined with your theater, if this does not solve your happiness problem, it should go a long way.
You're probably going to want to get rid of your Theater once you hit LMA, but until then- or unless you come by another event building or something offering better happiness- you should keep the theater. If you have, or come by the Innovation Tower GB take care not to level it too high or you'll have to get more happiness.
Also, check your city for any buildings that are increasing your population. If you can do without any of them, get rid of them (store them if valuable...)