I went into the plugin files for Smart YouTube and commented out the loading of jquery. I found it in smartyoutube.php, lines 97 and 98, and commented them out:
//$script_path = $this->plugin_url . '/javascripts/jquery.colorbox-min.js';
//wp_register_script( 'colorbox', $script_path );
This issue can be resolved by commenting out the line mentioned by SmoothAssault
Find this file:
/wp-content/plugins/jquery-colorbox/includes/jquery-colorbox-backend.php
On line 211, change:
$modifiedArray[‘theme_advanced_styles’] .= ‘;colorbox-link=colorbox-link;’;
to:
//$modifiedArray[‘theme_advanced_styles’] .= ‘;colorbox-link=colorbox-link;’;
that will remove the link from the Styles dropdown and allow the custom styles to appear