What you are talking about is an automated deployment strategy. They usually don't use cpanel at all and typically require at least shell access if not a dedicated server.
I've got no idea what your developers are building, but at least you'll need a way to:
a) Package the code for production -- ie, production settings and configuration options like the production database server
b) Generate and execute database migrations to update your database schema to the new schema
c) Some automated tests to make sure everything took
And probably some automated backup before all this goes down.