Add a custom stock status in WooCommerce

for anyone interested, here is complete solution, based on Laila's approach. Warning! My solution is intended to work only with WooCommerce "manage stock" option disabled! I am not working with exact amounts of items in stock. All code goes to functions.php, as usual.

Back-end part

Removing native stock status dropdown field. Adding CSS class to distinguish my new custom field. Dropdown has now new option "On Request".

function add_custom_stock_type() {
    ?>
    <script type="text/javascript">
    jQuery(function(){
        jQuery('._stock_status_field').not('.custom-stock-status').remove();
    });
    </script>
    <?php   

    woocommerce_wp_select( array( 'id' => '_stock_status', 'wrapper_class' => 'hide_if_variable custom-stock-status', 'label' => __( 'Stock status', 'woocommerce' ), 'options' => array(
        'instock' => __( 'In stock', 'woocommerce' ),
        'outofstock' => __( 'Out of stock', 'woocommerce' ),
        'onrequest' => __( 'On Request', 'woocommerce' ), // The new option !!!
    ), 'desc_tip' => true, 'description' => __( 'Controls whether or not the product is listed as "in stock" or "out of stock" on the frontend.', 'woocommerce' ) ) );
}
add_action('woocommerce_product_options_stock_status', 'add_custom_stock_type');

Sadly, WooCommerce will save only "instock" or "outofstock" values with its native functions. So after all product data processing, I have to re-save my stock status again.

function save_custom_stock_status( $product_id ) {
    update_post_meta( $product_id, '_stock_status', wc_clean( $_POST['_stock_status'] ) );
}
add_action('woocommerce_process_product_meta', 'save_custom_stock_status',99,1);

Template part

And the last thing - I have to alter data returned by product get_availability() function. When "managing stock" is off, WooCommerce only knows "instock" and "outofstock" values, again. So I have check stock status on my own.

function woocommerce_get_custom_availability( $data, $product ) {
    switch( $product->stock_status ) {
        case 'instock':
            $data = array( 'availability' => __( 'In stock', 'woocommerce' ), 'class' => 'in-stock' );
        break;
        case 'outofstock':
            $data = array( 'availability' => __( 'Out of stock', 'woocommerce' ), 'class' => 'out-of-stock' );
        break;
        case 'onrequest':
            $data = array( 'availability' => __( 'On request', 'woocommerce' ), 'class' => 'on-request' );
        break;
    }
    return $data;
}
add_action('woocommerce_get_availability', 'woocommerce_get_custom_availability', 10, 2);

Maybe it's not bulletproof solution ... I will update it, eventually.