How do I get Safari 9 to use my new pinned tab icon?

Safari is very keen to cache these icons, and indeed the lack of them. Once it has decided there is (or is not) an icon on your site, it will retain that knowledge, potentially for a very long time, and no amount of restarting or refreshing will change that.

You can encourage it to re-check for icons by deleting the contents of the following folder:

~/Library/Safari/Template Icons

And then restarting Safari.