There are a couple of ways to add in a Favicon Icon into a Genesis Child Theme, either filed in a folder or declared as a function. You can also set different favicons for certain pages.

File in Images Folder

You can add it the favicon in your WordPress themes folder inside your child theme images folder, filed as favicon.ico:

/wp-content/themes/genesischild/images/favicon.ico

Declare as a Function

Or alternatively you can add it via a function in your functions.php file and then you can file it anywhere

function genesischild_favicon( $favicon_url ) {
return 'http://mydomain.com/images/favicon.ico';
}

add_filter( 'genesis_pre_load_favicon', 'genesischild_favicon' );

The function is used with a variable and the variable is set to where the favicon is filed.

To add another different Favicon to a Different Page

Use a function with conditionals,

function genesischild_favicon_different( $favicon_url ) {
if (is_single('') && in_category('201') )
return 'http://mydomain.com/images2/favicon.ico'; 
} 

add_filter( 'genesis_pre_load_favicon', 'genesischild_favicon_different' );

So here to add a different favicon to a particular page, you could for example set a single post that belongs to a certain category which will use a different favicon. Here a string of conditionals are used, of course just one can be used instead.