A new experimental setup for simultaneous P-wave velocity (V_P) and density (ρ) measurements for liquid alloys is developed using ultrasonic and X-ray absorption methods combined with X-ray tomography at high pressures and high temperatures. The new setup allows us to directly determine adiabatic bulk moduli (K_S) and to discuss the correlation between the V_P and ρ of the liquid sample. We measured V_P and ρ of liquid Ni₆₈S₃₂ up to 5.6GPa and 1045K using this technique. The effect of pressure on the V_P and ρ values of liquid Ni₆₈S₃₂ is similar to that of liquid Fe₅₇S₄₃. (Both compositions correspond to near-eutectic ones.) The obtained K_S values are well fitted to the finite strain equation with a   value (K_S at ambient pressure) of 31.1GPa and a dK_S/dP value of 8.44. The measured V_P was found to increase linearly with increasing ρ, as approximated by the relationship: V_P [m/s]=1.29ρ [kg/m³] – 5726, suggesting that liquid Ni–S follows an empirical linear relationship, Birch's law. The dV_P/dρ slope is similar between Ni₆₈S₃₂ and Fe₅₇S₄₃ liquids, while the V_P–ρ plot of liquid Ni–S is markedly different from that of liquid Fe–S, which indicates that the effect of Ni on Birch's law is important for understanding the V_P–ρ relation of planetary and Moon's molten cores.