How to periodically run a script inside a fresh Docker container on Amazon AWS?

I have a Docker image for a web app which needs a specific script to be run once a day. The web app is going to be deployed to a web tier in Elastic Beanstalk. What would be the best way to create a container for this image in order to run the script and then remove this container?

Ideally, I'd like to have some easy way to do the following every 24 hours: Create a worker environment in Elastic Beanstalk with a new Docker container, run the script and remove the worker environment. But this doesn't seem possible.

I've found a few services in AWS that might help (Simple Workflow, OpsWorks, Data Pipeline), but seem massively complicated for what I want.

Any suggestions?