The *Costa Concordia* wasn't sunken, it was aground. Which meant that part of it was still above the water. The ping pong solution can only be used if the ship is *completely underwater*. Otherwise, it will have an *opposite* effect.

The buoyant force (force by which a fluid pushes up on a body, thus keeping it afloat), is proportional to the mass of the fluid displaced by the body. Thus, it can also be said to be proportional to the volume of the body that is submerged. Adding a ping pong ball to a floating ship will make it heavier, without changing the volume underwater (OK, it will sink a bit, changing the volume underwater, but that doesn't help us). Adding a ping pong ball to a ship that's aground has no use whatsoever.

On the other hand, a ship that is underwater is full of water. Adding a ping pong ball to the ship will force out some water, $\implies$ more water displaced $\implies$ more buoyant force. The reason this is better than pumping air is that air can easily excape, ping-pong balls can't.

![Costa concordia][1] 
Adding a ping pong ball here would just make it float inside the ship. It wouldn't displace any water.
[1]:http://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Costa-barrier.svg/220px-Costa-barrier.svg.png