Basically you have to set the cookie with a expiry date in the past. This does the trick.
As it needs to be in the past, I normally use a constant date:
$expiry = gmmktime(0,0,0, // hms
1, // month
1, // day
2005 // year
);
setcookie(AUTH_COOKIE_NAME, 'Delete',
$expiry, // expiry
'/'); // path
Mark