So I decided to make this quick guide after I saw a bunch of single cobble generators used on Skyblock. This is meant to be used on your starting island with the tiny little space it has, and generates 3 cobble instead of 1, with the usual 1/3 likelihood that the cobble gets burned. Once you have more space, I'm sure other designs are more efficient.
Start by facing west (use f3 to tell which direction you're facing, and _make sure_ to face west!), and make and fill a 3x4x1 hole with the sand as reference point to the middle, then break ice at the space in the hole closest to you to make water:
Then make dig a row deeper where the center row is (again where the sand is), and then block the water so it only goes into that row:
Finally, place lava at the farther end (west side) and dig two holes as shown.
To mine, just mine and walk back and forth between the two side holes. You MUST have the lava face west so when cobble forms while you're mining, it'll will always knock you towards the water and never towards the lava. I haven't tested north and south, but west is perfectly fine, so. Also, use a stone pick to do this. Wood picks won't be fast enough to mine it before the cobble knocks you off.
Hopefully people figure how inefficient single generators are; I'm still baffled as to why people use them at all