Firstly, a constructor method is "__construct()". Secondly, "$this" refers to the current object, not another object. Thirdly, you actually need to populate your variables.
PHP Code:
class League
{
private $vbulletin;
public function __construct($vbulletin)
{
$this->vbulletin = $vbulletin;
}
public function showNews()
{
echo $this->vbulletin->userinfo['username'];
}
}