How do I set a specific template for sub-categories?

I would recommend using the category_template filter – just check if the current category is an ancestor of 67:

function wpse_179617_category_template( $template ) {
    if ( cat_is_ancestor_of( 67, get_queried_object_id() /* The current category ID */ ) )
        $template = locate_template( 'category-slider.php' );
    return $template;
}

add_filter( 'category_template', 'wpse_179617_category_template' );