I don't know of any CMS that can handle something like that out of the box. It's different than a standard e-commerce interface since you have to reverse the transaction after a period of time.
I would look into a few things... possibly PHP through a solution like Drupal or a custom app framework like CakePHP or Zend. You might also consider some other app framework like Rails, Node.js, Django, etc. depending on your willingness to learn and what fits the project for you. It's a bit more custom so it sounds like you'll need an actual app framework instead of a CMS (but a CMS can still work; you're just going to have to code either way - in the instance of something like Drupal you will need custom modules and extensions to Views to make it work).
I would also ask what would make this site different than the one you linked to? Your competitive advantage can help steer you to the correct tool.