How to deploy a Docker image from a private repository on Cloud Foundry?
Using cf CLI 6.28.0 or higher, run cf push myapp -o bspartifact.artifactory.example.com/bspartifact:1.0 --docker-username myuser. This will prompt you for your password.
For non-interactive use, set environment property CF_DOCKER_PASSWORD to your password and the CLI will use that.
Refer to the following documentation for details: http://docs.cloudfoundry.org/devguide/deploy-apps/push-docker.html#private-repo
As mentioned from dkoper - you have to use cf CLI 6.28.0 or higher. But your Cloud Foundry provider should also support this. The feature to push docker images was implemented with Cloud Foundry api version 2.82.0. You can check on which api version your Cloud Foundry provider is running with cf api.