Magento 1.9 Email – Change New User Account Confirmation Email

That's not possible out of the box.
The password can be sent only when the user creates the account because that's the only time when you have the password in clear text.
Once it is saved in the db and you lose the customer instance you cannot get back the password because it is hashed.
But anyway, it's not a good practice to send the password via e-mail in clear text.
The customer should already know his password, and if he forgets it he can click on "Forgot my password"

Take a look at Magento Migrate customers with no password.

$customer = Mage::getModel('customer/customer');

$password = '123456';
$email = 'testuser@test.com';

$customer->setWebsiteId(Mage::app()->getWebsite()->getId());
$customer->loadByEmail($email);

if($customer->getId()) { // if customer does not already exists, by email

    $newPassword = $customer->generatePassword(); // generate a new password
    $customer->changePassword($newPassword); // set it
    $customer->save();    
}

Assuming that you want to use the default magento password template then take a look at app/code/core/Mage/Adminhtml/controllers/CustomerController.php

// Send welcome email
if ($customer->getWebsiteId() && (isset($data['account']['sendemail']) || $sendPassToEmail)) {
    $storeId = $customer->getSendemailStoreId();
    if ($isNewCustomer) {
        $customer->sendNewAccountEmail('registered', '', $storeId);
    } elseif ((!$customer->getConfirmation())) {
    // Confirm not confirmed customer
            $customer->sendNewAccountEmail('confirmed', '', $storeId);
    }
}