I am wanting to download an entire album from within the backend of Zen Photo. Is this possible?

I am ultimately trying to migrate specific albums from one Zen Photo installation to another new Zen Photo installation in a different directory.

Can anyone help?

Sorry, there is no function for this. The albums itself are file system based so you can just move/copy the folder representing an album via FTP. However any data entered manually on the backend will be lost when moving.

Maybe a way would be to temporarily move/copy the whole install?:
http://www.zenphoto.org/news/moving-and-changing-existing-installations/
Then afterwards you could delete the albums you don't want to use on the new install.