Using tag to output text in Genesis?

You can hook in the banner using the the_content_more_link filter by modifying this code.

add_filter( 'the_content_more_link', 'sp_read_more_link' );
function sp_read_more_link() {
return '<a class="your-banner" href="' . get_permalink() . '">[Banner Shortcode]</a>';
}

Another option would be to create a shortcode for your banner, and add the shortcode to the the_content_more_link filter above.

Or you could simply echo the div class and/or HTML for the banner in a custom function with or without a conditional tag.

add_filter( 'the_content_more_link', 'read_more_link' );
function read_more_link() {
if ( is_single() ) {
echo '<div class="your-banner">Add Your Banner HTML Here</div>';
    }
}

Either add HTML for your banner or create a shortcode otherwise the code does nothing.