  In granular superconductors, individual grains can contain bound Cooper pairs
while the system as a whole is strongly insulating. In such cases the
conductivity is determined by electron hopping between localized states in
individual grains. Here we examine a model of hopping conductivity in such an
insulating granular superconductor, where disorder is assumed to be provided by
random charges embedded in the insulating gaps between grains. We use computer
simulations to calculate the single-electron and electron pair density of
states at different values of the superconducting gap $\Delta$, and we identify
"triptych" symmetries and scaling relations between them. At a particular
critical value of $\Delta$, one can define an effective charge $\sqrt{2}e$ that
characterizes the density of states and the hopping transport. We discuss the
implications of our results for magnetoresistance and tunneling experiments.
