Creating a simple pagination for custom post type templates

I have custom post post type call 'news' and I am struggling to get it to paginate correctly. I'm looking for a simple prev and next links, not worried about page numbers in the middle.

In page-news.php this is my code:

<?php
    $paged = get_query_var('paged') ? get_query_var('paged') : 1;
    $args = array('post_type' => 'news', 'posts_per_page' => 2, 'paged' => $paged);
    $loop = new WP_Query( $args );
    while ( $loop->have_posts() ) : $loop->the_post();
?>

// Loop

<?php endwhile; wp_reset_postdata(); ?>

<div id="pagination" class="clearfix">
    <?php posts_nav_link(); ?>
</div>

The above code is showing 2 posts, but no pagination links

This is my custom post type code:

function custom_post_news() {
    register_post_type( 'news',
        array('labels' => array(
            'name' => __('News', 'post type general name'), /* This is the Title of the Group */
            'singular_name' => __('News', 'post type singular name'), /* This is the individual type */
            'add_new' => __('Add New', 'custom post type item'), /* The add new menu item */
            'add_new_item' => __('Add New'), /* Add New Display Title */
            'edit' => __( 'Edit' ), /* Edit Dialog */
            'edit_item' => __('Edit'), /* Edit Display Title */
            'new_item' => __('New '), /* New Display Title */
            'view_item' => __('View'), /* View Display Title */
            'search_items' => __('Search news'), /* Search Custom Type Title */
            'not_found' =>  __('Nothing found in the Database.'), /* This displays if there are no entries yet */
            'not_found_in_trash' => __('Nothing found in Trash'), /* This displays if there is nothing in the trash */
            'parent_item_colon' => ''
        ), /* end of arrays */
            'description' => __( 'This is the example custom post type' ), /* Custom Type Description */
            'public' => true,
            'publicly_queryable' => true,
            'exclude_from_search' => false,
            'show_ui' => true,
            'query_var' => true,
            'menu_position' => 2, /* this is what order you want it to appear in on the left hand side menu */
            'capability_type' => 'post',
            'hierarchical' => false,
            'rewrite' => array('slug' => 'news', 'with_front' => true ),
            /* the next one is important, it tells what's enabled in the post editor */
            'supports' => array( 'title', 'editor', 'thumbnail')
        )
    );

}


// REGISTER TAXOMONIES

add_action( 'init', 'custom_post_news');
register_taxonomy( 'custom_news',
    array('news'), /* if you change the name of register_post_type( 'movies', then you have to change this */
    array('hierarchical' => true,
        'labels' => array(
            'name' => __( 'News Categories' ), /* name of the custom taxonomy */
            'singular_name' => __( 'news Category' ), /* single taxonomy name */
            'search_items' =>  __( 'Search news Categories' ), /* search title for taxomony */
            'all_items' => __( 'All news Categories' ), /* all title for taxonomies */
            'parent_item' => __( 'Parent news Category' ), /* parent title for taxonomy */
            'parent_item_colon' => __( 'Parent news Category:' ), /* parent taxonomy title */
            'edit_item' => __( 'Edit news Category' ), /* edit custom taxonomy title */
            'update_item' => __( 'Update news Category' ), /* update title for taxonomy */
            'add_new_item' => __( 'Add New news item' ), /* add new title for taxonomy */
            'new_item_name' => __( 'New Custom news' ) /* name title for taxonomy */
        ),
        'show_ui' => true,
        'query_var' => true,
    )
);

This is a custom theme (started from scratch) so there's nothing in my functions.php referring to a pagination. I've scoured the Internet for answers, but I get a different solution and nothing seems to work.

I also don't have an archive-news.php as I'm not sure if this needs to be implemented or not?