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 $L_{rm CO(1-0)}-L_{rm 12mu m}$ 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.
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