For those who were interested in an answer to this question, I found the answer myself.
<div class="coda-slider" id="slideshow">
<?php
// array of category IDs
$categories = array(1,2,3,4,5);
foreach ($categories as $cat) :
$post = false;
$post = get_posts('cat=".$cat."&posts_per_page=1');
if($post) :
$post = $post[0];
setup_postdata($post); ?>
<!-- rest of normal loop -->
<div <?php post_class(); ?>>
<h2 class="title">title used to dynamically generate thumbs in codaslider</h2>
<h3><a href="https://wordpress.stackexchange.com/questions/71760/<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h3>
<?php the_content(); ?>
</div>
<?php endif; ?>
<?php endforeach; ?>
</div>
The original foreach loop code came from this post: