We measure the transverse relaxation of the spin state of an ensemble of ground-state rubidium atoms trapped in solid parahydrogen at cryogenic temperatures. We find the spin dephasing time of the ensemble (T$_2^*$) is limited by inhomogeneous broadening. We determine that this broadening is dominated by electrostatic interactions with the host matrix, and can be reduced by preparing nonclassical spin superposition states. Driving these superposition states gives significantly narrower electron paramagnetic resonance lines and the longest reported electron spin $T_2^*$ in any solid-phase system other than solid helium.