Adding content to a taxonomy metabox

From core:

function post_tags_meta_box($post, $box) {
    $defaults = array('taxonomy' => 'post_tag');
    if ( !isset($box['args']) || !is_array($box['args']) )
        $args = array();
    else
        $args = $box['args'];
    extract( wp_parse_args($args, $defaults), EXTR_SKIP );
    $tax_name = esc_attr($taxonomy);
    $taxonomy = get_taxonomy($taxonomy);
    $disabled = !current_user_can($taxonomy->cap->assign_terms) ? 'disabled="disabled"' : '';
    $comma = _x( ',', 'tag delimiter' );
?>
<div class="tagsdiv" id="<?php echo $tax_name; ?>">
    <div class="jaxtag">
    <div class="nojs-tags hide-if-js">
    <p><?php echo $taxonomy->labels->add_or_remove_items; ?></p>

As you can see, there is no hook. So the only options are JavaScript or a clone of the metabox.

Third option: Open a Trac ticket and ask for a new hook.

You could also use output buffering, but I don’t recommend that, especially on that page.