Bounty noted.  I am actually working on it right now.

EDIT: Okay, I am ready to claim.  Since you said private key, and not a WIF key or public key, its actually pretty easy.

Here is the method, which requires two dice or any other randomizing method.  Roll the two six sided dice 64 times.  Right down the numbers like this:

If the number is 0-9 right now the number.  If the number is 10-12 right now a-c.  Do this with each roll of the dice and you will get a valid hex private key, such as A9 87 3C 79 B6 D8 70  A0 1B 61 57 78 63 33 89 B4 45 32 13 30 3A A6 1C 20 CC 67 2C 23 36 B3 32 62

This is a valid bitcoin private key.  Note that this does not use all the hex characters, and as such can not generate all possible private keys, but its easy to do with just two dice.

You could also buy a 16 sided dice or something and use 0-F which would be more proper.  If you do it this way, the max address you can use is FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141