The metals being sonorous has deep connections with their damping capacity which is lower as compared to non-metals. This implies that the impulse vibrations that create the sound to last longer. This would become clear through a careful analysis of stress-strain analysis of metals.
For metals under small loads, the stress and strain are in phase. The phase angle $\delta$ is given by $$\tan\delta=\frac{E''}{E'}$$ where $E''$ is the loss modulus and $E'$ is the storage modulus. So for metals, the phase angle is (nearly) zero. So the loss modulus is zero and the loading and unloading curves are superposed on each other. This means that the intervening area is zero and there is no hysteresis loss. Thus low loss modulus means that there is low damping which in turn means that metals are sonorous.