Retrieve file from folder and save to different folder on daily basis

I've got a photography site which the owner wants to have the 'featured image' to be frequently changed. I seek some kind of scripts that randomly picks an image from folder images/portfolio/full/ and copies it to folder images/homepage/ with the name homepage.jpg on a daily basis.

Is this easily achieveable? I could ask the hosting provider to create a cron job, but unknown if the would agree to that.

Looking forward to a method to achieve this!