This can be easily done by creating a counter, here is the updated code:
<h2>Recent News</h2>
<ul class="post-carousel">
<?php
$posts = get_posts("showposts=10");
if ($posts) {
$counter=0;
foreach ( $posts as $post) : setup_postdata($post);
echo ($counter % 2 ==0) ? '<li>':'';?>
<div class="entry">
<div class="entry-date">
<div class="entry-day"><?php the_time('d'); ?></div>
<div class="entry-month"><?php the_time('M'); ?></div>
</div>
<div class="entry-body">
<h4 class="entry-title"><a href="<?php the_permalink() ?>"><?php the_title(); ?></a></h4>
<div class="entry-content">
<div class="content">
<?php echo wp_trim_words(apply_filters('the_excerpt', $post->post_content), $num_words = 55); ?>
</div>
<p><a href="<?php the_permalink() ?>">Read More ›</a></p>
</div>
</div>
</div>
<?php echo ($counter % 2 == 1) ? '</li>': '';
$counter++;
endforeach;
}
echo ($counter % 2 == 1) ? '</li>': '';
?>
</ul>