List child categories from parent category on custom taxonomy page

Two things!

1) Don’t use query_posts()! Instead, for situations like this, use the pre_get_posts action to modify the query.

2) I don’t think you actually want to be using a loop here at all (so neither query_posts() nor pre_get_posts or even WP_Query). Rather, I think you’re looking for wp_list_categories. In your template, you’d probably do something like this (untested):

<?php
// the taxonomy archive term page's term id
$queried_object = get_queried_object();
$term_id = $queried_object->term_id;

$list_child_terms_args = array(
    'taxonomy' => 'YOUR_CUSTOM_TAXONOMY_SLUG_HERE',
    'use_desc_for_title' => 0, // best practice: don't use title attributes ever
    'child_of' => $term_id // show only child terms of the current page's
);
?>
<ul>
    <?php wp_list_categories( $list_child_terms_args ); ?>
</ul>