The UNIX time being stored in your DB comes from the server hosting your database.
So, for the site that is in a different time zone, you need to adjust for the 8 hours difference. You can do this by using switch or an if statement to find the HTTP_HOST and then add (or subtract) the time difference for the one that is different.
Example:
$fixdate = $datefromdatabase;
$siteHost = getenv('HTTP_HOST');
// If [url]http://www.playwork.co.uk/diary.php[/url] is 8 hours ahead add 8 hours to the date.
if($siteHost == "playwork.co.uk") {
$fixdate = $fixdate + (3600*8);
}