If your main slideshow works, but not a carousel, you are missing the Cycle2 Carousel plugin, which is necessary for the desired functionality. Find it on the Cycle2 download page
http://malsup.imtqy.com/min/jquery.cycle2.carousel.min.js
EDIT
The correct way to queue scripts is to take care of the dependencies in the parameters wp_enqueue_script().
, , . , script.
function my_scripts_method() {
$template_dir = get_template_directory_uri();
if ( is_page('home') ){
wp_enqueue_script( 'cycle2', $template_dir . '/js/jquery.cycle2.min.js',array( 'jquery' ) );
wp_enqueue_script( 'cycle2-carousel', $template_dir . '/js/jquery.cycle2.carousel.min.js', array( 'jquery', 'cycle2' ) );
}
}
add_action( 'wp_enqueue_scripts', 'my_scripts_method' );
, , html , .