You could have a simple script written (although there may be one already. Check [url]http://hotscripts.com[/i]) that would take the contents of a directory and make a page with the contents as links on it. You then wrap it with HTML code for the look and feel of the site. Getting the files to the directory could be with an FTP program, set up to launch with the necessary setting already in place. Conversely you could have a second script written that would take a file and put it in the correct location on the server.
You should be able to get a custom script for this pretty inexpensively if you post the job on one of the freelance sites (like http://getafreelancer.com. Neither is a difficult thing to write.