I really like this plugin! Personal Favicon works on Multisite installs of WordPress.
I simply created a directory (folder) in my Public HTML directory, and inside that, I created more directories for each of my sub sites. I placed the chosen favicon files into these directories. Then, I simply linked each Personal Favicon install in each of the sub sites to their respective favicons in the favicon directories.
I was really glad to see that although I performed a Network Activation of Personal Favicon, I still had the option whether or not to activate it on each of the sub sites.
Good work to the creator of Personal Favicon!