  In a recent experiment [A. Donarini et al., Nat Comms 10, 381 (2019)],
electronic transport through a carbon nanotube quantum dot was observed to be
suppressed by the formation of a quantum-coherent ``dark state''. In this paper
we consider theoretically the counting statistics and waiting-time distribution
of this dark-state-limited transport. We show that the statistics are
characterised by giant super-Poissonian Fano factors and long-tailed
waiting-time distributions, both of which are signatures of the bistability and
extreme electron bunching caused by the dark state.
