The solution is Fudge dice. These six-sided three-dimensional randomizers have three symbols repeated twice and lend themselves to the random generation of alignments better than the original alignment dice themselves. [Fudge dice have six sides that are marked "+" on two sides, "-" on two sides, and left blank on two sides.] For one thing, they are not merely inked, they are incised, which means they last forever. For another thing, only a single Fudge die is necessary, since the "+" and "-" symbols can double as Lawful vs. Chaotic and Good vs. Evil.
For those who like charts, voila:
|1st dF||2nd dF|
Combined, we may generate the following results:
|+||Lawful Good||Lawful Neutral||Lawful Evil|
|0||Neutral Good||True Neutral||Neutral Evil|
|-||Chaotic Good||Chaotic Neutral||Chaotic Evil|
Incidentally, all alignment dice are Chaotic. Use them at your own risk.
[Originally posted here in Fudgerylog.]