There is probably a much cleaner way of doing this using off-the-shelf automations.  But I was just following along with the AWS installation instructions and got this working.

- name: Download AWS CLI bundle.
shell: "cd /tmp && rm -rf /tmp/awscli* && curl 'https://s3.amazonaws.com/aws-cli/awscli-bundle.zip' -o 'awscli-bundle.zip'"

- name: Update repositories cache and install "unzip" package
apt:
name: unzip
update_cache: yes

- name: Unzip AWS CLI bundle.
shell: "cd /tmp && unzip awscli-bundle.zip"

- name: Run AWS CLI installer.
shell: "/tmp/awscli-bundle/install -i /usr/local/aws -b /usr/local/bin/aws"

- name: Log into aws ecr docker registry
when: jupyterhub__notebook_registry != ''
shell: "$(/usr/local/bin/aws ecr get-login --no-include-email --region us-east-1)"

In order to do the actual login, you need to ensure your EC2 instance has an IAM role assigned to it that has reader privileges. Then you should be all good!