  We formalize the derivation of a generalized coarse-graining $n$-resolved
master equation by introducing a virtual detector counting the number of
transferred charges in single-electron transport. Our approach enables the
convenient inclusion of coherences and Lamb shift in counting statistics. As a
Markovian example with Lindblad-type density matrices, we consider the
Born-Markov-Secular (BMS) approximation which is a special case of the
non-Markovian dynamical coarse graining (DCG) approach. For illustration we
consider transport through two interacting levels that are either serially or
parallelly coupled to two leads held at different chemical potentials. It is
shown that the coherences can strongly influence the (frequency-dependent)
transport cumulants: In the serial case the neglect of coherences would lead to
unphysical currents through disconnected conductors. Interference effects in
the parallel setup can cause strong current suppression with giant Fano factors
and telegraph-like distribution functions of transferred electrons, which is
not found without coherences. We demonstrate that with finite coarse graining
times coherences are automatically included and, consequently, the shortcomings
of the BMS approximation are resolved.
