How about "millibits". That's short. It's rather catchy, and (at least to someone that speaks english with a Chicago accent) it rolls of the tongue nicely.
It sounds good, but "bits" is already in use for "100 Satoshis". That makes 1 millibit 0.000000001
BTC. Kilobits could actually work, it has the the same as millibitcoin, but sounds better.