Changing the signature to

public static function create(ContainerInterface $container)

Changing the signature to static

    namespace Drupal\livequotes\Controller;
use Drupal\Core\Entity\EntityInterface;
use Drupal\Core\Controller\ControllerBase;

/**
 * Controller routines for livequotes routes.
 */

class LivequotesController extends ControllerBase{
    
    protected $entity;

    public static function create(Container $container) {
        return new static($container->get('entity'));
    }
    
    public function __construct(EntityInterface $em) {
        $this->entity = $em;
    }
    /**
     * Re-render a specific block (yeah if we do something it should be generic).
     */
    public function livequotesShowBlock() 
    {
        $block_id = "livequotes_content";
        $block = $this->entity->getStorage('block')->load($block_id);
        return $this->entity->getViewBuilder('block')->view($block);
    }
}

UPDATE 4

Changing the signature to

public static function create(ContainerInterface $container)

results in the following error:

Declaration of Drupal\livequotes\Controller\LivequotesController::create() must be compatible with Drupal\Core\DependencyInjection\ContainerInjectionInterface::create(Symfony\Component\DependencyInjection\ContainerInterface $container)