Blue-green deployment to heroics or another cloud platform as a service

We are currently launching a two-speaker Ruby on Rails project (RefineryCMS) on Heroku.

Each time we update the site, the downtime is from 1 to 2 minutes. Managers are unhappy with this.

What we really need is some kind of (transparent) blue-green deployment: http://martinfowler.com/bliki/BlueGreenDeployment.html

Is it possible to achieve this on Heroku or another cloud platform as a service?

We also use Unicorn, but will gladly change if necessary.