AAAA I'M SO MAD!! I had this thread all typed out, but when I pressed "Create Thread" it redirected to the login page. I hit login, and then my thread was completely gone. So I had to retype it all. Please fix this glitch, I really hate it.
Anyway, let's get to my suggestion.
Under layer 16, there is a small chance (~2%) that a block of coal ore that generates will instead generate as a diamond ore. This means that in the occasional vein of coal, there might be a diamond sticking out against the other coal ores. So if you mined 5 full veins of coal, each with 20 ores, you could expect to get only 2 diamonds (assuming all veins were under layer 16)
IMPORTANT: It's only individual coal ore blocks that generate as diamond, NOT entire veins! That would be too OP.
At y=15, there is a 0.2% chance for a diamond to spawn instead of coal.
y=14 ----- 0.4%
y=13 ----- 0.6%
y=3 ----- 2.6%
y=2 ----- 2.8%
y=1 ----- 3.0%
This suggestion is based on the misconception that diamonds can be created by putting coal under pressure. This is not really correct. Although they are both carbon based substances, coal has a lot of impurities, but diamond is pretty much pure carbon. Even if you did have a lump of carbon, you'd need to subject it to insane temperatures (~3000 C) and extreme pressures (~100000 atmospheres) to turn it into diamond. That's one thing Minecraft got right: diamonds only generate deep underground.