airflow.hooks.docker_hook.DockerHook is using docker_default connection where one isn't configured.

Now in your first attempt, you set google_con for docker_conn_id and the error thrown is showing that host (i.e registry name) isn't configured.

Here are a couple of changes to do:

• image argument passed in DockerOperator should be set to image tag without registry name prefixing it.

DockerOperator(api_version='1.21',
    # docker_url='tcp://localhost:2375', #Set your docker URL
    command='/bin/ls',
    image='image',
    network_mode='bridge',
    task_id='docker_op_tester',
    docker_conn_id='google_con',
    dag=dag,
    # added this to map to host path in MacOS
    host_tmp_dir='/tmp', 
    tmp_dir='/tmp',
    )

• provide registry name, username and password for the underlying DockerHook to authenticate to Docker in your google_con connection.

You can obtain long lived credentials for authentication from a service account key. For username, use _json_key and in password field paste in the contents of the json key file.

Here are logs from running my task:

[2019-11-16 20:20:46,874] {base_task_runner.py:110} INFO - Job 443: Subtask docker_op_tester [2019-11-16 20:20:46,874] {dagbag.py:88} INFO - Filling up the DagBag from /Users/r7/OSS/airflow/airflow/example_dags/example_docker_operator.py
[2019-11-16 20:20:47,054] {base_task_runner.py:110} INFO - Job 443: Subtask docker_op_tester [2019-11-16 20:20:47,054] {cli.py:592} INFO - Running <TaskInstance: docker_sample.docker_op_tester 2019-11-14T00:00:00+00:00 [running]> on host 1.0.0.127.in-addr.arpa
[2019-11-16 20:20:47,074] {logging_mixin.py:89} INFO - [2019-11-16 20:20:47,074] {local_task_job.py:120} WARNING - Time since last heartbeat(0.01 s) < heartrate(5.0 s), sleeping for 4.989537 s
[2019-11-16 20:20:47,088] {logging_mixin.py:89} INFO - [2019-11-16 20:20:47,088] {base_hook.py:89} INFO - Using connection to: id: google_con. Host: gcr.io/<redacted-project-id>, Port: None, Schema: , Login: _json_key, Password: XXXXXXXX, extra: {}
[2019-11-16 20:20:48,404] {docker_operator.py:209} INFO - Starting docker container from image alpine
[2019-11-16 20:20:52,066] {logging_mixin.py:89} INFO - [2019-11-16 20:20:52,066] {local_task_job.py:99} INFO - Task exited with return code 0