OK, I admit: it's not all that amazing, and it doesn't really disappear (it just folds up), and it's not much of a "coffee table;" more of a teeny little end-table/foot stool. But it does give me a place to put my feet/netbook/coffee/breakfast/etc while I'm preventing the couch from levitating, and it does fold up and hide quite nicely.

Step 1: Materials

Materials:
Two 18" lengths of 2"x2"
Two 5" lengths of 2"x2"
One 15" dowel (I used an old broom handle)
One 3" metal rod
Two 12" squares (for the base & top). I used 1"x12" pine shelving (plywood would be fine, too)
Two hinges (almost any size or style will work). Note: Four would provide less wobbly results.
Short wood screws: enough for the hinges
Four long wood screws: about 2"

Tools:
Saw
Drill
Small drill bit (for pilot holes)
1" drill bit (or: just a little bigger than the dowel)
1/2" drill bit (or: just a little bigger than the metal rod)

Step 2: Build The... "legs"

(...for lack of a better noun).
Drill a 1/2" hole through the middle of the wooden dowel.
Drill a 1/2" hole into the middle of each 18" 2x2, about one inch deep.

Screw the 5" 2x2s onto both ends of one of the 18" 2x2s (drill pilot holes to prevent splitting).

Slide the metal rod through the dowel and into one of the 18" 2x2s.
Slide the second 18" 2x2 onto the metal rod.

Attach the remaining 18" 2x2, ensuring that the dowel spins freely.

Sit around spinning the dowel freely for a while. Important: make airplane and/or helicopter noises.

Step 3: Hinges

Mount the hinges to allow the base and tabletop to be flush with the 2x2s when horizontal.
Two hinges would result in more stability.

Step 4: Drill "pockets" for the Dowel

Drill a 1" hole for the dowel in the bottom of the tabletop, and in the top of the base.

I'm sure the location and angle could be determined by mathematics, but I guessed: swing the dowel out so that the table is level, and mark the spot with a pencil. Drill the holes at the dowel's angle, and sink them deep enough so that the dowel does not slip out when a little weight is applied.

Step 5: Fold & Stow... Unfold & Enjoy!

To fold for storage, simply lift the tabletop, swing the dowel into its 2x2 "frame," and lay flat. Mine fits under my couch.

Other ideas:
Add a cushion for a comfy footstool: mine is a tiny bit wobbly due to the inherent "play" one finds in most hinges; adding another pair of hinges or ones built to more exacting standards would result in more stability. But the strength is more than sufficient, since a heavier weight pushes the dowel more securely into the boards.

Use nice wood (as evidenced by the photos, the wood I used was crappy).

Paint/inlay a chess board.

Sink coasters into the surface for an even more beverage-friendly table.

Integrate snaps or magnets or straps to hold it all closed, and a handle for portability.

Integrate snaps or magnets or straps to hold it all open, for added stability.

Sit on it (more robust construction recommended).

Build something else entirely: The "legs" of this stool could be adapted to a variety of applications. The "X" created by a middle piece that swings out allows for a compact support system.

Thanks for reading, and best of luck with your 'ibles!