Quantity   Component name
1 × 3 Axis Accelerometer I was looking at the Freescale MMA8452Q (Sparkfun has a breakout board for prototyping: https://www.sparkfun.com/products/12756) . It has some nice features like a freefall and tap detection that could wake a sleeping microprocessor.
6 × Displays The first one I have found that is small enough is the Kingbright ACDA02-41SURKWA-F01 (I forgot where I found that). They have to be small enough to fit into a dice size package. I might make these with surface mount LEDs. If anyone can suggest a small display I could use (at least 2 characters), that would be a big help!
1 × Shift Register? If the processor is small, it might not have too many outputs to drive the displays. A shift register or two might help address the problem.
1 × Microprocessor The BBRRRAAAAIINNNSSSS.... Probably an ATtiny85 (https://www.sparkfun.com/products/9378) or something like this. It doesn't need to be overly powerful, depending on what kind of displays can be found. Having the Arduino bootloader would allow for easy modification later as well. Dip package for prototyping, then onto surface mount.
1 × Battery A small Lithium battery would be perfect. They fit one into the fitbit, so I think i can fit one into dice.
1 × Battery charger If you got a Lithium battery, you might need a lithium battery charger chip so it doesn't explode. I could use a TI BQ24040 (its the one in the fitbit).
1 × Bluetooth This I think will be the most difficult part to work with. I've never done anything with bluetooth beyond pairing a couple of devices. The fitbit uses the Nordic Semiconductor nRF8001, that might work. I have to figure out how to prototype with these tiny chips.
1 × Cool Case You can't show all the guts to the world, so you need a case to cover all this stuff and allow a perfect rolling experience. 3D print it? Probably.