Genesis has a function called genesis_load_favicon that searches the Child theme's folder for an ico, gif, png, or jpg favicon file (e.g., favicon.ico, favicon.gif, favicon.png, favicon.jpg). It also has a filter for the URL and a filter to short-circuit the entire function.
Once you’ve made your new custom favicon.ico (Use photoshop to make a small png or use this plugin/add-on), upload it to your child theme’s images directory.
Or, if you have a network of sites and want to pull a favicon from somewhere else, you can use this function in your functions.php file.
After you have done one of these two things, you may still see the Genesis favicon and think your favicon has not been changed. However, trust me, it has been changed and your cache is causing the issue. If you really, really want to see it immediately, then clear the cache in all your browsers, close all web applications, restart computer, and be patient. Or, just call/contact someone else to check for you.