Magento – Cash on delivery method not showing

The method is enabled and it shoud stay like that.

There is no reason to keep it enabled in the store if you don't show it in the frontend. If you need it enabled for backend orders, configure it as enabled in the default configuration and as disabled in the websites or store view configuration.

AS i have seen in your reference link you can also see

code for

1) table rates shipping method == flatrate_flatrate

2) cash on delivery" payment method. == cashondelivery

EDIT

class Mage_Shipping_Model_Carrier_Tablerate
    extends Mage_Shipping_Model_Carrier_Abstract
    implements Mage_Shipping_Model_Carrier_Interface
{

    /**
     * code name
     *
     * @var string
     */
    protected $_code = 'tablerate';
}

Simple Magento shipping method code

<pre>Array
(
    [0] => Array
        (
            [value] => Array
                (
                    [0] => Array
                        (
                            [value] => flatrate_flatrate
                            [label] => Fixed
                        )

                )

            [label] => Flat Rate
        )

    [1] => Array
        (
            [value] => Array
                (
                    [0] => Array
                        (
                            [value] => freeshipping_freeshipping
                            [label] => Free
                        )

                )

            [label] => Free Shipping
        )

    [2] => Array
        (
            [value] => Array
                (
                    [0] => Array
                        (
                            [value] => tablerate_bestway
                            [label] => Table Rate
                        )

                )

            [label] => Best Way
        )

    [3] => Array
        (
            [value] => Array
                (
                )

            [label] => Best Way
        )

)

i am sure it will help you.