While Saharsh's answer appears to give you the results in the format you want - it's a very expensive query.
Since you've cited your expected output as a serialized PHP array, this implies that you're using PHP to process the data. A much more efficient approach is to use the following query then merge the data into a PHP array:
SELECT rtype, DATE_FORMAT(iperiod, '%b %e') AS period, amount
FROM
(SELECT 'chat' AS rtype,
COUNT(id) as amount,
DATE(timestamp) as iperiod
FROM tblChats
WHERE timestamp BETWEEN '{$start}' AND '{$end}'
AND UserID = 0
GROUP BY DATE(timestamp)
UNION
SELECT 'mail' as rtype,
COUNT(id) as mail_amount,
DATE(timestamp) as iperiod
FROM tblMails
WHERE timestamp BETWEEN '{$start}' AND '{$end}'
AND UserID = 0
GROUP BY DATE(timestamp)) ilv
ORDER BY period DESC;
BTW: DATE_FORMAT(timestamp, '%b %e') will not produce '2012-11-09', and does the DESC modifier work on a GROUP BY expression?