In a small superconducting electrode connected to a reservoir via a Josephson junction, we can realize an artificial two-level system in which two charge-number states of the electrode are coupled by Cooper-pair tunneling. We have investigated quantum coherence in the two-level system through two complementary experiments: (i) photon-assisted Cooper-pair-tunneling spectroscopy of the energy-level splitting in the frequency domain, and (ii) pulsed-gate control of the quantum state to observe the coherent oscillations in the time domain. Our results demonstrate the existence and the persistence of the coherence for at least ∼30 cycles of the oscillation.