Pagination on category page with custom post types

Before I go to your problem, I would like to start of by asking why you are using a custom query on a category page instead of the main query. You should never change the main query for a custom query on any archive page or on your home page.

WordPress provides an action hook, pre_get_posts which you can use in conjunction with conditional tags to target and modify the main query before it is executed on specific pages. For category pages the is_category() conditional check is supplied.

You could just simply do the following in your functions.php, while keeping your default loop in tact on your category page. Just a tip, pre_get_posts uses the same parameters as WP_Query

function add_news_to_category( $query ) {
    if ( !is_admin && $query->is_category() && $query->is_main_query() ) {

         $query->set( 'post_type', array( 'news' ) );
         $query->set( 'posts_per_page', '9' );
         $query->set( 'orderby', 'date' );

    }
}
add_action( 'pre_get_posts', 'add_news_to_category' );

OK, now to your actual problem with your code.

• Firstly, you don’t need to use wp_reset_query and wp_reset_postdata together. wp_reset_query is actually used in conjunction with query_posts, which you must never use, and I mean never. Just simply use wp_reset_postdata afterWP_Queryandget_posts`, and remember, never forget to do that

• Secondly, look closer at your code. You have $query = new WP_Query( $args_news );, but then you have <?php next_posts_link( 'Older Posts', $custom_query->max_num_pages ); ?>. Spot the difference? $query and $custom_query. So, <?php next_posts_link( 'Older Posts', $custom_query->max_num_pages ); ?> should be <?php next_posts_link( 'Older Posts', $query->max_num_pages ); ?>

For further reading:

• When to use a custom query and when to use the main query