We study intrinsic noise of current in a superconducting single-electron tr
ansistor, taking into account both coherence effects and Coulomb interactio
n near a Cooper pair resonance. Because of this interplay, the statistics o
f tunneling events deviates from the Poisson distribution and, more importa
nt, it shows even-odd asymmetry in the transmitted charge. The zero-frequen
cy noise is suppressed significantly when the quasiparticle tunneling rates
are comparable to the coherent oscillation frequency of Cooper pairs.