Version:
minecolonies-1.12.2-0.10.28-ALPHA

Expected behavior

I accidentally killed a citizen with my epic sword and the happiness dropped to 1.
The happiness should then rise every day by a certain number and to a certain number.

Actual behaviour

The happiness is at 1 for 3 days now.

Do I just need to wait a little longer or what?

Depending on your colony it may or may not (depending how happy your citizens are, there are some indications in the townhall and in the GUIs of the citizen)