CloudBees support Play dists natively - with Jenkins and continuous deployment - you can read more about this here - yes, you can run it for free.
How to use:
- Signup for CloudBees (if you don't already have an account)
- Run the ClickStart to setup a working Play app, with repo and Jenkins build service
- Clone the repo created above - push your changes and then glory is yours !
Alternatively, you may want to just deploy from your Play command shell directly (using SBT), the plugin for this can be found here.