I'm not sure how much this solves your problem of "deploying docker containers" but our service Quay.io can be used to push/pull/serve your private binary image

I'm not sure how much this solves your problem of "deploying docker containers" but our service Quay.io can be used to push/pull/serve your private binary images. Couple that with something like Digital Ocean's Docker image, and you can deploy docker containers pretty simply.