  Using 53 pb$^{-1}$ of $e^+e^-$ annihilation data taken at $\sqrt{s}=3.686$
GeV, a comprehensive study has been made of the radiative decays of samples of
5.1 million $J/\psi$ and 24.5 million $\psi(2S)$ into pairs of pseudoscalar
mesons, $\pi^+\pi^-$, $\pi^0\pi^0$, $K^+K^-$, $K_S^0K_S^0$, and $\eta\eta$.
Product branching fractions for the radiative decays of $J/\psi$ and $\psi(2S)$
to scalar resonances $f_0(1370,1500,1710,2100, \text{and} 2200)$, and tensor
resonances $f_2(1270,1525, \text{and} 2230)$ have been determined, and are
discussed in relation to predicted glueballs. For $\psi(2S)$ radiative decays
the search for glueballs has been extended to masses between 2.5 GeV and 3.3
GeV.
