Record the existing container id, rescale the service to 2 instances (hence bringing a second container up), wait for the second one to be healthy, (optional) stop directing traffic to the old container, wait a few seconds, stop the old container, rescale the service back to 1 instance.
Blue Green Deployment. There must be a docker container to handle this or at least a bash script.
edit: thanks to next comment for referencing one
Here's a CLI plugin that automates this: https://github.com/wowu/docker-rollout