here's simple php code to list most comment nodes in certain period of time. This example use to list most comment node in the past week only.

//it's unix timestamp value. within past week can be translated to 60 x 60 x 24 x 7 = 604800 seconds
// more info about unix timesamp http://en.wikipedia.org/wiki/Unix_time
$period = 604800;
//limit node to list
$limit = 5;

$sql = "SELECT node.nid, node_comment_statistics.comment_count AS comment_count, node.created, node.title FROM {node} node  LEFT JOIN {node_comment_statistics} node_comment_statistics ON node.nid = node_comment_statistics.nid WHERE node.type='story' AND node.created > (UNIX_TIMESTAMP() - ".$period.") ORDER BY comment_count DESC, node.created DESC LIMIT ".$limit;

$result = db_query($sql);
if (db_num_rows($result)) {
    $most_comment = '<ul>';
    //loop each node
	while ($node = db_fetch_object($result)) {
        $link = 'node/'.$node->nid;
        $most_comment .= '<li>'.l($node->title,$link).'</li>';
    }
    $most_comment .= '</ul>';
}
echo $most_comment;

you can modify sql slightly to have different queery, i.e: between specific period time, exact date, etc by changing this part (UNIX_TIMESTAMP() - ".$period.")

or alternatively, you can use views with date range filter