Magento – Add Discount coupon code box on checkout page in magento 1.9

Open your theme files checkout.xml in layout app/design/frontend/YOUR_PACKAGE/YOUR_THEME/layout/checkout.xml

You can see code for replace that code with below:

<checkout_onepage_index translate="label">
    <label>One Page Checkout</label>
    <!-- Mage_Checkout -->
    <remove name="left"/>

    <reference name="root">
        <action method="setTemplate"><template>page/2columns-right.phtml</template></action>
    </reference>
    <reference name="right">
        <action method="unsetChildren"></action>
        <block type="page/html_wrapper" name="checkout.progress.wrapper" translate="label">
            <label>Checkout Progress Wrapper</label>
            <action method="setElementId"><value>checkout-progress-wrapper</value></action>
            <block type="checkout/onepage_progress" name="checkout.progress" before="-" template="checkout/onepage/progress.phtml">
                <block type="checkout/onepage_progress" name="billing.progress" template="checkout/onepage/progress/billing.phtml"></block>
                <block type="checkout/onepage_progress" name="shipping.progress" template="checkout/onepage/progress/shipping.phtml"></block>
                <block type="checkout/onepage_progress" name="shippingmethod.progress" template="checkout/onepage/progress/shipping_method.phtml"></block>
                <block type="checkout/onepage_progress" name="payment.progress" template="checkout/onepage/progress/payment.phtml"></block>
        <block type="checkout/cart_coupon" name="checkout.cart.coupon" as="coupon" template="checkout/cart/coupon.phtml"/> 
            </block>

        </block>
    </reference>
    <reference name="content">
        <block type="checkout/onepage" name="checkout.onepage" template="checkout/onepage.phtml">
            <block type="checkout/onepage_login" name="checkout.onepage.login" as="login" template="checkout/onepage/login.phtml">
                <block type="page/html_wrapper" name="checkout.onepage.login.before" as="login_before" translate="label">
                    <label>Login/Registration Before</label>
                    <action method="setMayBeInvisible"><value>1</value></action>
                </block>
            </block>
            <block type="checkout/onepage_billing" name="checkout.onepage.billing" as="billing" template="checkout/onepage/billing.phtml"/>
            <block type="checkout/onepage_shipping" name="checkout.onepage.shipping" as="shipping" template="checkout/onepage/shipping.phtml"/>
            <block type="checkout/onepage_shipping_method" name="checkout.onepage.shipping_method" as="shipping_method" template="checkout/onepage/shipping_method.phtml">
                <block type="checkout/onepage_shipping_method_available" name="checkout.onepage.shipping_method.available" as="available" template="checkout/onepage/shipping_method/available.phtml"/>
                <block type="checkout/onepage_shipping_method_additional" name="checkout.onepage.shipping_method.additional" as="additional" template="checkout/onepage/shipping_method/additional.phtml"/>
            </block>
            <block type="checkout/onepage_payment" name="checkout.onepage.payment" as="payment" template="checkout/onepage/payment.phtml">
                <block type="checkout/onepage_payment_methods" name="checkout.payment.methods" as="methods" template="checkout/onepage/payment/info.phtml">
                    <action method="setMethodFormTemplate"><method>purchaseorder</method><template>payment/form/purchaseorder.phtml</template></action>
                </block>
                <block type="core/template" name="checkout.onepage.payment.additional" as="additional" />
                <block type="core/template" name="checkout.onepage.payment.methods_additional" as="methods_additional" />
            </block>
            <block type="checkout/onepage_review" name="checkout.onepage.review" as="review" template="checkout/onepage/review.phtml"/>
        </block>
    </reference>
</checkout_onepage_index>

And put the following code in app/design/frontend/YOUR_PACKAGE/YOUR_THEME/template/checkout/onepage/progress.phtml

<div class="block block-progress opc-block-progress<?php if (!$this->isCustomerLoggedIn()/* && !$this->getCheckout()->getStepData('billing', 'is_show')*/): ?> opc-block-progress-step-login<?php endif; ?>">
<div class="block-title">
    <strong><span><?php echo $this->__('Your Checkout Progress') ?></span></strong>
</div>
<div class="block-content">
    <dl>
        <?php if ($this->getCheckout()->getStepData('billing', 'is_show')): ?>
        <div id="billing-progress-opcheckout">
            <?php echo $this->getChildHtml('billing.progress') ?>
        </div>
        <?php endif; ?>

        <?php if ($this->getCheckout()->getStepData('shipping', 'is_show')): ?>
        <div id="shipping-progress-opcheckout">
            <?php echo $this->getChildHtml('shipping.progress') ?>
        </div>
        <?php endif; ?>

        <?php if ($this->getCheckout()->getStepData('shipping_method', 'is_show')): ?>
        <div id="shipping_method-progress-opcheckout">
            <?php echo $this->getChildHtml('shippingmethod.progress') ?>
        </div>
        <?php endif; ?>

        <?php if ($this->getCheckout()->getStepData('payment', 'is_show')): ?>
        <div id="payment-progress-opcheckout">
            <?php echo $this->getChildHtml('payment.progress') ?>
        </div>
        <?php endif; ?>

    <?php echo $this->getChildHtml('coupon') ?>
    </dl>
</div>

You can see below screenshot for result:

Then clear cache and check.