Display your own Favicon in Genesis Child Themes.

genesis-favicon.php

/** Adding My custom Favicon
* (change www.mywebsite.com with your website url)
*/
add_filter( 'genesis_pre_load_favicon', 'my_custom_favicon' );
function my_custom_favicon( $favicon_url ) {
	return 'http://www.mywebsite.com/images/favicon.png';
}

// or better use relative URL 

/** Adding My custom Favicon 
* (change child-theme-name with your child theme name)
*/
add_filter( 'genesis_pre_load_favicon', 'my_custom_favicon' );
function my_custom_favicon( $favicon_url ) {
	return ''. trailingslashit( get_bloginfo('url') ) .'/wp-content/themes/child-theme-name/images/favicon.png';
}