  We report the measured production rates of unstable isotopes $^9$Li and
$^8$He produced by cosmic muon spallation on $^{12}$C using two identical
detectors of the RENO experiment. Their beta-decays accompanied by a neutron
make a significant contribution to backgrounds of reactor antineutrino events
in precise determination of the smallest neutrino mixing angle. The mean muon
energy of its near (far) detector with an overburden of 120 (450) m.w.e. is
estimated as 33.1 +- 2.3 (73.6 +- 4.4) GeV. Based on roughly 3100 days of data,
the cosmogenic production rate of $^9$Li ($^8$He) isotope is measured to be
44.2 +- 3.1 (10.6 +- 7.4) per day at near detector and 10.0 +- 1.1 (2.1 +- 1.5)
per day at far detector. This corresponds to yields of $^9$Li ($^8$He), 4.80 +-
0.36 (1.15 +- 0.81) and 9.9 +- 1.1 (2.1 +- 1.5) at near and far detectors,
respectively, in a unit of 10$^{-8}$ $\mu^{-1}$ g${^-1}$ cm${^2}$. Combining
the measured $^9$Li yields with other available underground measurements, an
excellent power-law relationship of the yield with respect to the mean muon
energy is found to have an exponent of $\alpha$ = 0.75 +- 0.05.
