I finally found 2 diamond blocks in a mine I had almost given up for lost because when I started it, I went through 4 stone pickaxes without finding anything more than about 2 blocks of coal, and maybe 2 redstone blocks with the next 4 picks.

In the end, I just kept going down until I hit the unbreakable stuff and then went in a 2x2 straight line forever (probably 15 pickaxes at least) picking up what I found along the way with my iron axe (the diamonds, more redstone, a little gold, a little iron).

Right when I was about to give up for the night (I used up my last pickaxe and last torch at about the same moment and it's a loooooong walk back to the top, I heard running water, so I went back for 4 more picks and more torches so I could explore. I just tried to follow the sound which put me in a little danger of getting lost...twice I hit straight into lava and had to quickly throw down some stone blocks to keep from getting hit by it. Eventually I found a tiny cavern where a lava flow and water flow are adjacent, and also managed to find 3 blocks of obsidian (at the risk of flooding of the mine by digging upwards, although it seems you can place blocks inside water to plug up a hole, because that's what I did).

Also, I have a double-chest full of stone block stacks now. What should I do with it?