So what's left? I turn you back the remark: I'm not sure why you have that few of a problem.
Sam's right, you're wrong. But let's try to figure out why. You should NEVER need to use the Avoid Growth option, if you're playing correctly, because you should always have a small Happiness surplus to account for that growth.
1> How many luxuries do you have within your territory? That's actually two questions: how many UNIQUE luxuries, and how many total luxury deposits?
In most games, you'll start with 4-5 different types of luxury within reach "your" territory, one of which will have clustered deposits (meaning extras). You SHOULD be able to trade those extras away for two or three additional luxuries.
2> Have you bribed any city-states into alliances, or conquered any? When the game is starting, three luxury resources are reserved ONLY for city-states. Only after starting locations are determined are these resources placed, so you should be making an attempt to get these somehow.
3> Which policy branches have you unlocked? As he pointed out, every branch now has at least SOME Happiness. Piety is no longer the main Happiness-changer (at least in the vanilla game) with the change to Theocracy, but it's still got Organized Religion (+1 Happy per Monument, Temple, or Monastery); Monasteries will only be in a few cities, but those others should be in every city you have, so that's +2 per city right there. And other branches can do even better; the Honor branch can now get FIVE happiness per city from two consecutive policies...
4> Have you been building every available Happiness-producing building in every city? I don't just mean the Colosseum. Did you notice the Stone Works generating +1 Happiness? Or the Circus Maximus adding 5? A Circus (+2)? There are quite a few of these less common sources of Happiness out there.
So post your numbers. That is, the Happiness pulldown in the upper-left; take a screenshot if you want, or write it down, so that we can see how many Happiness you're gaining from luxuries, buildings, etc., and how many Unhappiness you're generating from number of cities and population.
The thing is, before this last patch the main source of Happiness was luxuries. One new luxury equalled one new city, easily making up the small disparity between the building happiness and the Unhappiness generated by size. Given the +9 you start with, that meant that 4-5 luxuries could support 6-7 cities fairly easily. (Add another for the Circus Maximus, and once you got to Theocracy...)
Post-patch, luxuries aren't nearly enough and you're expected to take Policies that help with this, most of which key off of specific buildings or playstyles.
Now, given that we're in the modding forum here, it's simple to point out that quite a few mods (including my own) tweak a lot of this. In my mod, cities generate even MORE Unhappiness (4 + 1.2/pop instead of 3+1/pop), but I've got a half-dozen more buildings that add +1 Happiness. It's even more of a challege staying above 0 in my mod, and yet the people who play it can do so fairly consistently.