Add class to every other posts using get_posts

A simple solution would be to add an alternating class to every other post in the list. In particular, (in your style.css) style the list elements <li> in one particular way, and then over-ride that style for list elements of a particular class <li class="my-alternate-class">. The class my-alternate-cass will applied to every other list element:

<?php global $post;
    $args = array('post_type' => 'events');
    $custom_posts = get_posts($args);
    if($custom_posts):?>
         <ul>;
         <?php foreach($custom_posts as $post) : setup_postdata($post);?>
              <?php $class = (empty($class) ? "class="my-alternate-class"" : "");?>
              <li <?php echo $class;?>>Content goes here</li>
         </ul>;
         <?php endforeach; ?>
    <?php endif; ?>
    //Remember to wp_reset_postdata() afterwards
    wp_reset_postdata();
?>

Please note this untested.

I’ve also added wp_reset_postdata() as otherwise your site might break.