Most of CD including deployments already works for private projects, it is only the auto deploy https://docs.gitlab.com/ee/ci/autodeploy/index.html that doesn't work yet. We would all like to see auto deploy working with private projects and it is scheduled for 9.1

If you don't want to use GitLab.com to host your code you can install GitLab yourself or use the mirroring function in GitLab to deploy code hosted elsewhere.