If the private image is in a registry which does not require authentication you can just use the registry url in the Docker image field.
If your registry requires authentication, it becomes a little more complicated.
You will need to set up a script on the agent server which will run the docker login command. (in ~/.profile for example)
docker login -u <myuser> -p <mypassword> registryurl
Once this is configured and the remote agent has sourced the new script, it will be able to connect to the private image registry. You can test this by attempting a docker pull for your desired image.
You will need to configure the above for all remote agents which will need to connect to the private registry.