This idea is much more entertaning than it is practical. It is an underwater venture.

Construct an object made of two ballons, that are tied together. They are made from a very sturdy fabric. This material is flexible, but it won't fail, rip apart or so, even under great pressures.

In one of the ballons, put powdered carbon, very pure. Actually, it is better if  you can place many small ballons with carbon. 

In the other, put two substances that when mixed, for a gas as a product. It shouldn't be a very fast reaction, though, you don't mean it for be explosive. These substances would mix when a counter reaches an end. You would have to devise a contraption for them to mix just when the coundown is over.

Add a GPS locator to this object. This device is heavily shielded to go to great depths.

Now sail to the Marianas Trench, one of the deepest spots in the oceans in our World, set the timer and drop the devices on the water. 

It sinks all the long way to the sea floor, to incredible water pressures. Once the timer has elapsed, the ballon will start to fill with gases, the object's density will decrease and it will start to float back to the surface, slowly.

As it reaches the surface, engage the GPS to get its location and salvage it.

Hopefully, you will find out that there were diamonds formed on the pouches.