Below is a php code to create a credit memo for an order in magento.

$order = Mage::getModel('sales/order')->load('100000001', 'increment_id');
        if (!$order->getId()) {
            $this->_fault('order_not_exists');
        }
        if (!$order->canCreditmemo()) {
            $this->_fault('cannot_create_creditmemo');
        }
        $data = array();

       
        $service = Mage::getModel('sales/service_order', $order);
      
        $creditmemo = $service->prepareCreditmemo($data);

        // refund to Store Credit
        if ($refundToStoreCreditAmount) {
            // check if refund to Store Credit is available
            if ($order->getCustomerIsGuest()) {
                $this->_fault('cannot_refund_to_storecredit');
            }
            $refundToStoreCreditAmount = max(
                0,     min($creditmemo->getBaseCustomerBalanceReturnMax(), $refundToStoreCreditAmount)
            );
            if ($refundToStoreCreditAmount) {
                $refundToStoreCreditAmount = $creditmemo->getStore()->roundPrice($refundToStoreCreditAmount);
                $creditmemo->
setBaseCustomerBalanceTotalRefunded($refundToStoreCreditAmount);

                $refundToStoreCreditAmount = $creditmemo->getStore()->roundPrice(
                    $refundToStoreCreditAmount*$order->getStoreToOrderRate()
                );
                // this field can be used by customer balance observer
                $creditmemo->setBsCustomerBalTotalRefunded($refundToStoreCreditAmount);
                // setting flag to make actual refund to customer balance after credit memo save
                $creditmemo->setCustomerBalanceRefundFlag(true);
            }
        }
        $creditmemo->setPaymentRefundDisallowed(true)->register();
        // add comment to creditmemo
        if (!empty($comment)) {
            $creditmemo->addComment($comment, $notifyCustomer);
        }
        try {
            Mage::getModel('core/resource_transaction')
                ->addObject($creditmemo)
                ->addObject($order)
                ->save();
            // send email notification
            $creditmemo->sendEmail($notifyCustomer, ($includeComment ? $comment : ”));
        } catch (Mage_Core_Exception $e) {
            $this->_fault('data_invalid', $e->getMessage());
        }
        echo $creditmemo->getIncrementId();