  We study intrinsic noise of current in a superconducting single-electron
transistor, taking into account both coherence effects and Coulomb interaction
near a Cooper-pair resonance. Due to this interplay, the statistics of
tunneling events deviates from the Poisson distribution and, more important, it
shows even-odd asymmetry in the transmitted charge. The zero-frequency noise is
suppressed significantly when the quasiparticle tunneling rates are comparable
to the coherent oscillation frequency of Cooper pairs.
