Since there is no init system running in the container, the only process running in the container is postgres itself, so docker restart container-name or docker kill -sTERM container-name followed by docker start container-name will work.

As long as you are not running the process with docker run -it --rm ..., or doing docker rm after you stop it, then the container's data will stick around and you can start it up again.

What if we want to do something in the container while it's running? Like for instance move Postgresql into /dev/shm so tests run superfast in RAM. You need to stop and restart Postgresql while the container is up for that or the RAM disk gets deleted.

I thought maybe I could try

su - postgres -c '/usr/lib/postgresql/9.6/bin/pg_ctl stop -D /var/lib/postgresql/data'
cp -r /var/lib/postgresql/data /dev/shm
su - postgres -c '/usr/lib/postgresql/9.6/bin/pg_ctl -D /dev/shm start'

But my container exits immediately after running the first line

I tried to restart the Postgres while it had one active connection. Now I'm not able to start it again. Is there anyway I can start it? I don't want to loose any data :(

I wrote up how to do this extensively a while back, it might help:
https://richardcooke.info/how-to-run-your-tests-against-an-in-memory-database-with-a-rails-rspec-mysql-example/
and
https://stackoverflow.com/questions/42226418/how-to-move-postresql-to-ram-disk-in-docker

You can run postgres in background (by supervisor for example), or set restart policy in compose file.

For the ramdisk use-case, I usually start another container to keep the ramdisk around appropriately, ala:

$ docker volume create \
--driver local \
--opt type=tmpfs \
--opt device=tmpfs \
--opt o=size=1048576k \
my-new-volume

When starting PostgreSQL:

$ docker run ... -v my-new-volume:/var/lib/...

When I want to restart PostgreSQL or re-create the container:

$ docker run -d --name temp -v my-new-volume:/save-me:ro alpine:3.7 top
$ docker stop my-postgres
$ docker run ...
$ docker rm -f temp

Since the original question is answered, I'm going to close.

As is stumbled upon the same problem a few minutes ago:
su - postgres -c "PGDATA=$PGDATA /usr/lib/postgresql/10/bin/pg_ctl -w restart"
in case of version 10, worked for me ;) 👍

@SeWieland , your command will restart the container. It's not as smooth as nginx's nginx -s reload.

Command below is the perfect command to avoid restart and most importantly does not disrupt ongoing queries

$ docker exec -it {postgres_container}  psql -U postgres -c "SELECT pg_reload_conf();"

@Dean-Christian-Armada thank you! That was exactly what I searched for.
And it is actually the accurate answer to the original question.

Calling pg_reload_conf() will only reload parameters which don't require a restart to update. [Source]
For this reason, a restart remains a viable option for cases where configuration options can't be reloaded.

But still, this proves to be useful on some configurations rather than restarting a container and having downtime

login with postgres user, and
execute "SELECT pg_reload_conf()".

To reload the config, you can login with postgres user and run the reload command

su postgres
/usr/lib/postgresql/9.5/bin/pg_ctl reload