Where do you want to call it? Whithin the model's class or whitin another controller's class? Anyway you can use dependency injection

controller method within model class

public function yourMethodWhitinTheModelClass(OrderController $controller)
{
    return $controller->mailInvoice($this->id);
}

got error:

Argument 2 passed to Orders::autoPay() must be an instance of OrderController, none given, called in /var/www/haroldas.test.com/app/controllers/OrderController.php on line 137 and defined

function autoPay($user, OrderController $controller)
{
      // ...
      return $controller->mailInvoice($this->id);
}

got error:

Argument 2 passed to Orders::autoPay() must be an instance of OrderController, none given, called in (filename) on line (linenumber)

Aha! So you are passing a function call with only 1 variable, you need to add another variable:

function autoPay($user, OrderController $controller)
{
      $nowwhereismysecondvariableplease = object_instance_of_OrderController;
      return $controller->mailInvoice($this->id, $nowwhereismysecondvariableplease);
}

I would pass $controller as that variable ...

Better to invoke an event that the controller observes so you don't wind up with code that is unnecessarily bound.