Zero downtime deployments are just a side effect of doing any kind of A/B deployment.

The same features can help you avoid longer downtime. I use dokku at home to run a little web portal. I have a CHECKS file in the repo that has

  WAIT=1
  TIMEOUT=1
  ATTEMPTS=10
  / Portal
  ...

If I try to update to a new version and the site doesn't come up at all (or a GET for / doesn't have "Portal" in the response), the update is aborted and requests never fail.