The Atacama Large Millimeter/submillimeter Array (ALMA) has opened a new avenue to study the demographics of supermassive black holes (BHs) in nearby galaxies. Through ALMA observations at subarcsecond resolution, we have found dynamically cold, rotating, nuclear gas disks in a number of massive early-type galaxies. We present ALMA CO emission-line morphologies and kinematics for two radio-loud galaxies, NGC 315 and NGC 4261, both of which show rapid gas rotation arising from within the BH sphere of influence, where the BH dominates over the enclosed mass. We discuss gas-dynamical modeling that yield best-fitting BH masses of 2.08×109 Msun for NGC 315 and 1.68×109 Msun for NGC 4261, with respective statistical uncertainties of 0.5 and 6% that are dominated by modeling systematics of 10 and 25%. In the case of NGC 4261, the derived mass is a factor of 3 higher than the previously measured value from Hubble Space Telescope ionized gas kinematics, and we attribute the difference to the better spatial coverage of the ALMA data and improved dynamical modeling techniques. Such precision BH mass measurements are necessary to anchor the sparsely populated high-mass end of the BH mass-host galaxy relationships and allow for more confident probes of accretion physics in the most massive galaxies.