  We present CO(J=1-0) and/or CO(J=2-1) spectroscopy for 31 galaxies selected
from the ongoing MaNGA survey, obtained with multiple telescopes. This sample
is combined with CO observations from the literature to study the correlation
of the CO luminosities ($L_{\rm CO(1-0)}$) with the mid-infrared luminosities
at 12 ($L_{12 \mu m}$) and 22 $\mu$m ($L_{\rm 22 \mu m}$), as well as the
dependence of the residuals on a variety of galaxy properties. The correlation
with $L_{\rm 12 \mu m}$ is tighter and more linear, but galaxies with
relatively low stellar masses and blue colors fall significantly below the mean
$L_{\rm CO(1-0)}-L_{\rm 12\mu m}$ relation. We propose a new estimator of the
CO(1-0) luminosity (and thus the total molecular gas mass) that is a linear
combination of three parameters: $L_{\rm 12 \mu m}$, $M_\ast$ and $g-r$. We
show that, with a scatter of only 0.18 dex in log $(L_{\rm CO(1-0)})$, this
estimator provides unbiased estimates for galaxies of different properties and
types. An immediate application of this estimator to a compiled sample of
galaxies with only CO(J=2-1) observations yields a distribution of the
CO(J=2-1) to CO(J=1-0) luminosity ratios ($R21$) that agrees well with the
distribution of real observations, in terms of both the median and the shape.
Application of our estimator to the current MaNGA sample reveals a gas-poor
population of galaxies that are predominantly early-type and show no
correlation between molecular gas-to-stellar mass ratio and star formation
rate, in contrast to gas-rich galaxies. We also provide alternative estimators
with similar scatters, based on $r$ and/or $z$ band luminosities instead of
$M_\ast$. These estimators serve as cheap and convenient $M_{\rm mol}$ proxies
to be potentially applied to large samples of galaxies, thus allowing
statistical studies of gas-related processes of galaxies.
