  We analyze the charge dynamics of a superconducting single-electron
transistor (SSET) in the regime where charge transport occurs via Cooper-pair
resonances. Using an approximate description of the system Hamiltonian, in
terms of a series of resonant doublets, we derive a Born-Markov master equation
describing the dynamics of the SSET. The average current displays sharp peaks
at the Cooper-pair resonances and we find that the charge noise spectrum has a
characteristic structure which consists of a series of asymmetric triplets of
peaks. The strongest feature in the charge noise spectrum is the triplet of
peaks centered at zero frequency which has a peak spacing equal to the level
separation within the doublets and is similar to the triplet in the spectrum of
a driven, damped, two-level system. We also explore the back-action that the
SSET charge noise would have on an oscillator coupled to the island charge,
measurement of which provides a way of probing the charge noise spectrum.
