Perhaps the easiest thing to do would be to set up a Juicebox gallery using a Flickr account as the source of images.
The user could then simply upload new images to the Flickr account and they would automatically be included in the Juicebox gallery (without the need to modify any gallery files).
For reference, a list of all Flickr configuration options can be found on the Config Options page (in the Lite and Flickr sections).
Please note that the configuration options in the Flickr section are Pro only and not available in Juicebox-Lite.

It would also be possible to use a PHP script to instruct Juicebox to dynamically display all images in a designated folder.
Please see this forum post for details on how this could be achieved.

Both these methods work equally well with Juicebox-Lite and Juicebox-Pro so you could try them out with Juicebox-Lite (the free version) before purchasing Juicebox-Pro.
Juicebox-Lite can be downloaded from this web page.