We present near-infrared and optical observations of the Type Ic Supernova (SN) 2020oi in the galaxy M100 and the broad-lined Type Ic SN2020bvc in UGC 9379, using Gemini, LCO, SOAR, and other ground-based telescopes. The near-IR spectrum of SN2020oi at day 63 since the explosion shows strong CO emissions and a rising K-band continuum, which is the first unambiguous dust detection from a Type Ic SN. Non-LTE CO modeling shows that CO is still optically thick, and that the lower limit to the CO mass is 0.001 Msun. The dust temperature is 810 K, and the dust mass is ~10-5 Msun. We explore the possibilities that the dust is freshly formed in the ejecta, heated dust in the pre-existing circumstellar medium, and an infrared echo. The light curves of SN2020oi are consistent with a STELLA model with canonical explosion energy, 0.07 Msun Ni mass, and 0.7 Msun ejecta mass. A model of high explosion energy of ~1052 erg, 0.4 Msun Ni mass, 6.5 Msun ejecta mass with the circumstellar matter, reproduces the double-peaked light curves of SN2020bvc. We observe temporal changes of absorption features of the IR Ca II triplet, S I at 1.043 micron, and Fe II at 5169 Angstrom. The blue-shifted lines indicate high velocities, up to 60,000 km/s for SN2020bvc and 20,000 km/s for SN2020oi, and the expansion velocity rapidly declines before the optical maximum. We present spectral signatures and diagnostics of CO and SiO molecular bands between 1.4 and 10 microns.