Try using POST. The discount amount also needs to be in an array:
$id = $api->post("coupons", "add", array('code' => $coupon, 'company_id' => "1", 'max_qty' => "1", 'end_date' => "2013-11-17 03:59:59",'recurring' => "0", 'limit_recurring' => "0", 'packages' => array("10"), array(array('currency' => "USD", 'amount' => "100.0000"))))->response();