I know that in Magento 1.4.2.0 one gets parent id\'s like so
list( $parentId ) = Mage::getModel(\'catalog/product_type_configurable\')
You may use:
$product->getTypeInstance();
Which will return the type object of your product
Then you can perform your:
->getParentIdsByChild()
Giving finally:
$product->getTypeInstance()->getParentIdsByChild($child->getId());