We present results from an Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 2 program to map CO(2-1) emission in nearby early-type galaxies (ETGs) that host circumnuclear gas disks. We obtained $sim0.3-$resolution Band 6 observations of seven ETGs selected on the basis of dust disks in Hubble Space Telescope images. We detect CO emission in five at high signal-to-noise ratio with the remaining two only faintly detected. All CO emission is coincident with the dust and is in dynamically cold rotation. Four ETGs show evidence of rapid central rotation; these are prime candidates for higher-resolution ALMA observations to measure the black hole masses. In this paper we focus on the molecular gas and continuum properties. Total gas masses and H$_2$ column densities for our five CO-bright galaxies are on average $sim10^8$ $M_odot$ and $sim10^{22.5}$ cm$^{-2}$ over the $sim$kpc-scale disks, and analysis suggests that these disks are stabilized against gravitational fragmentation. The continuum emission of all seven galaxies is dominated by a central, unresolved source, and in five we also detect a spatially extended component. The $sim$230 GHz nuclear continua are modeled as power laws ranging from $S_ u sim u^{-0.4}$ to $ u^{1.6}$ within the observed frequency band. The extended continuum profiles of the two radio-bright (and CO-faint) galaxies are roughly aligned with their radio jet and suggests resolved synchrotron jets. The extended continua of the CO-bright disks are coincident with optically thick dust absorption and have spectral slopes that are consistent with thermal dust emission.
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