Display direct children of the current custom taxonomy in taxonomy.php template

See the Codex. The wp_list_categories allows you to set a child_of and a depth (in this case 1, we only want to go one level down).

See the link to the Codex about styling it; there’s a whole host of options.

<?php $term = get_queried_object();
     wp_list_categories(array(
       'taxonomy'=>$term->taxonomy,
       'child_of'=>(int) $term->term_id,
       'hide_empty'=>0,
       'depth'=>1,
  )); ?>

I’ve only tested this on built-in categories, but this should work for custom taxonomies too.