How can I generate a Minecraft world with no stone?

Solution 1:

As you said "natural selection of other blocks", you will not get any blocks. There is a complex formula that tells the game what blocks may spawn at what location, which includes depth.

In other words: It's not possible to get a natural selection of other blocks to replace the stone.

The custom generator for Minecraft allows you to generate worlds without stone, but you will have to define the exact layout of the world, which is not generated as you want it to be.

Last resort: A custom mod. Downsides to this are that you most likely cannot update your game and world if the game gets an update, without losing most of the new features, or without losing the functionality of the mod. Also, if you want to play with friends, you will need to host a server, which requires a lot more RAM compared to just sharing your world through the game client.

Solution 2:

You might want to use http://minecraft.tools/en/custom.php to generate a custom world with custom blocks, and then import it into your save or server folder.