How to output child links based on the current page
Just wanted to follow-up. I came back to this question and found the following: https://stackoverflow.com/questions/2716787/how-to-get-all-the-menu-items-below-a-certain-parent-in-drupal which is exactly what I needed.

The code, copied from the above-mentioned link and modified to fit my needs (mainly to use the current path to build the menu tree from, rather than using a hard-coded value:

$parent = menu_link_get_preferred($_GET['q']);
$parameters = array(
  'active_trail' =&gt; array($parent['plid']),
  'only_active_trail' =&gt; FALSE,
  'min_depth' =&gt; $parent['depth']+1,
  'max_depth' =&gt; $parent['depth']+1,
  'conditions' =&gt; array('plid' =&gt; $parent['mlid']),
);

$children = menu_build_tree($parent['menu_name'], $parameters);

return '&lt;div class="content-sub-menu content-padder"&gt;' . drupal_render(menu_tree_output($children)) . '&lt;/div&gt;';