You just got to be lucky. try making a mine the goes all the way down to bed rock then every so few steps you go back up, tunnle a mine going right or left is all you really can do to try to find diamonds!
Check out Cosmic Trigger (case sensitive). It's the one I play on all the time. Tons of iron and good amounts of diamonds as well as gold. The terrain has a little bit of everything too, mountains, desert, caves, scenic shorelines.
It's my first world, but I can't believe the luck I had with it so far. It's amazingly rich in resources (haven't seen snow yet, but with the way this map has surprised me I wouldn't be surprised if I rounded a corner into a snow drift.), but I've found
numerous dungeons with monster spawners, several pumpkins, lots of sugar cane, and of all the luck I actually built my first home structure literally on top of a massive underground cave system that spans across most of the map and has allowed me to discover
other caverns in the areas nearby as well. You literally cannot go down there without myself or another player who knows it as a guide because you will get lost for days down there. It's insanely huge and definitely fun to explore. There's lots of lava down
there and a few spawners.
At first when you spawn it would appear that there's nothing special about the place, few cactus', lots of sand, etc. but the more time I spent there I've discovered I actually had several forests, a few deserts complete with open lava right at the surface
level, and mountains that were a joy to dive off from into the ocean. One mountain has a waterfall coming out of it naturally so I actually just put the finishing touches on a subway system to get to allow myself and supplies to get there quickly so I can
begin constructing a massive castle just along side it.
But I digress...if anyone's curious you can enter the seed: eve
Several things: 1. If you want to explore that hellmouth of a cavern I accidently built my first home on, walk up from the spawn area, towards the ocean near a grassy overlook where you'll find lava pouring out of the cliff side naturally into the ocean.
I chose the spot because it had lava, water, and other resources naturally close by, never realizing the amount of resources buried underneath there and other locations. 2. Most of the treasures in this seed are quickly found simply digging down a bit.3. If
you don't want to dig, follow the shore lines to a forest nearby, there will be huge holes in various locations leading to other massive caverns, and one nearby cave with a spawner in it easily seen at night from the shore.
Chest has string, saddle, cocoa beans, iron ingot and gun powder. As for the world, great mountain range in the north, kinda flat and boring everywhere else. The diamond/lava problem, you just have to be lucky.