Looking for stop/start Postgresql hosting

I am looking for some PostgreSQL hosting for my app. As my site is being pre-built on the server into static files, I only need the database to be 'active' during the site build process, during development and when I'm uploading new data. That's probably only 5-10 hours a week I need the database to be usable, so I don't really want to me paying for a 24/7 service.

I'm currently using Azure, but there's no option to stop/start the database. I have to export a dump, delete the database, and re-create and import it if I want to start again. Too much hassle.

I think 20GB of space is more than enough. Does anyone have a suggestion for a cheap host? I don't really care at all about performance, reliability or support. Thanks