  We present simultaneous measurements of emission from dust continuum at 230
GHz and the J=2-1 $^{12}$CO, $^{13}$CO and C$^{18}$O isotopologues at $\sim$ 15
pc resolution from individual Giant Molecular Clouds (GMCs) in the Andromeda
galaxy (M31). These observations were obtained in an ongoing survey of this
galaxy being conducted with the Submillimeter Array (SMA). Initial results
describing the continuum and $^{12}$CO emission were published earlier. Here we
primarily analyze the observations of $^{13}$CO and C$^{18}$O emission and
compare them to the measurements of dust continuum and $^{12}$CO emission. We
also report additional dust continuum and CO measurements from newly added GMCs
to the M31 sample. We detect spatially resolved $^{13}$CO emission with high
signal-to-noise in 31 objects. We find the extent of the $^{13}$CO emission to
be nearly comparable to that of $^{12}$CO, typically covering 75\% of the area
of the $^{12}$CO emission. We derive $^{13}$CO and C$^{18}$O abundances of 2.9
$\times 10^{-6}$ and 4.4 $\times 10^{-7}$ relative to H$_2$, respectively, by
comparison with hydrogen column densities of the same regions derived from the
dust continuum observations assuming a Milky Way gas-to-dust ratio. We find the
isotopic abundance ratio [$^{13}$CO]/[C$^{18}$O] = 6.7$\pm$2.9 to be consistent
with the Milky Way value (8.1). Finally, we derive the mass-to-light conversion
factors for all three CO species to be $\alpha_{12} = 8.7 \pm 3.9$,
$\alpha_{13} = 48.9 \pm 20.4$ and $\alpha_{18} = 345^{+25}_{-31}$ M$_\odot$ (K
km s$^{-1}$pc$^2$)$^{-1}$ for the J=2-1 transitions of $^{12}$CO, $^{13}$CO and
C$^{18}$O, respectively.
