There are a lot of ways to improve stability:

Assigning a "governor" to a city.

Wonders.

Various infrastructures like "aqueduct".

Improving/obtaining luxuries.

There is also a district with the face mask icon (forgot its name).

There is also a city project later on that you execute (some kind of sports festival if I'm not mistaken).

So how high does stability need to be to get civics points?