Registered users can deploy recent SLES and RHEL instances. Since SLES12 SP1 along with the containers module provides Docker support, it's an easy way to play with Docker there. Try it!
The quickest way to get a container up is:
sudo -i service docker start
docker pull s390x/debian
docker run -ti s390x/debian bash
Make sure /var/lib/docker resides on /data to have some headroom when playing, unless it is already the case (e.g. mkdir /data/docker; rm /var/lib/docker; ln -s /var/lib/docker /data/docker -- note this will remove your local images).
Use the image of your choice from Docker hub -- searching there for s390x shows all the available images from various users. Images prefixed with s390x/ are the official builds, but there are a lot of interesting images from other users. Or you start creating your own base image (e.g. as described here or here). Enjoy!
Update: the next post was entirely done on that environment, by the way.