[jacques_chester]

I'm going to guess Heroku. They pioneered PaaSes, which are intended to solve this problem. Spoiler: they solve this problem.

There's also my fave, Cloud Foundry -- try Pivotal Web Services or BlueMix.

These PaaSes have a buildpack model and basically, it Just Works.

Or OpenShift, though maybe its shift to a pure docker-y model will put you back where you started.

Disclaimer: I work for Pivotal Labs, part of the company which donates the most engineering to Cloud Foundry.