It is fun to explain to kids that you have control over gravity.
How it works
The Cartesian diver contains a weight (which is more dense than water), and an air bubble (obviously, less dense than water). When the container is squeezed, the internal air pressure increases, and the size of the bubble decreases. As a result, the density of the diver changes from being less dense than water to being more dense than water and the diver sinks.
Thus, the Cartesian diver changes its density with changes in atmospheric pressure.
Making your own
What you need is a diver that just barely floats .. if it is too buoyant, then no matter how hard you squeeze you won't be able to make it sink. Therefore, I suggest that you balance your diver in a shallow bowl and then move it to the plastic bottle.
Divers can be made out of anything that can trap a bubble of air. Some people try to adjust the size of the bubble. Other people allow the diver to hold as much air as possible and then add weights (usually paper clips) until it barely floats.
Common diver materials
If the water is not all the way to the top of the bottle, surface tension may make it very difficult to make the diver sink. We have found that adding a piece of plastic or cork helps by not allowing the top of the diver to touch (actually, penetrate) the surface of the water. A drop of soap will also "break" (reduce) the surface tension.
With the right conditions - weight, bubble size, length of water column - you can create a diver that will not return to the surface. What happens is that, if the bottle is deep enough, when the pressure is released the bubble will not expand enough to make the diver lighter than water.
Have fun experimenting.