How to show more than 5 posts?

I think you could use the posts_per_page argument in your get_posts query:

$args = array( 'child_of' => 1 );
$categories = get_categories( $args ); 
foreach ($categories as $category) {
    echo '<li><a>'.$category->name.'</a>';
    echo '<ul>';

    $posts_args = array(
        'posts_per_page' => 9,
        'category' => $category->term_id
    );
    foreach (get_posts($posts_args) as $post) {
        setup_postdata( $post );
        echo '<li><a href="'.get_permalink($post->ID).'">'.get_the_title().'</a></li>';         
    }  
    echo '</ul></li>';
}