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We present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 5 and Cycle 6 observations of CO (2 -1) and CO (3-2) emission at 0"2-0"3 resolution in two radio-bright, brightest group/cluster early-type galaxies, NGC 315 and NGC 4261. The data resolve CO emission that extends within their black hole (BH) spheres of influence (rg), tracing regular Keplerian rotation down to just tens of parsecs from the BHs. The projected molecular gas speeds in the highly inclined (i ≥ 60°) disks rise at least to 500 km s-1 near their galaxy centers. We fit dynamical models of thin-disk rotation directly to the ALMA data cubes and account for the extended stellar mass distributions by constructing galaxy surface brightness profiles corrected for a range of plausible dust extinction values. The best-fit models yield (MBH/109 M⊙)= 2.08 ± 0.01(stat)+0.32-0.14 (sys) for NGC315 and (MBH/109 M⊙) = 1.67 ± 0.10(stat)+0.39-0.24(sys) for NGC 4261, the latter of which is larger than previous estimates by a factor of ~3. The BH masses are broadly consistent with the relations between BH masses and host galaxy properties. These are among the first ALMA observations to map dynamically cold gas kinematics well within the BH-dominated regions of radio galaxies, resolving the respective rg by factors of ~5-10. The observations demonstrate ALMA's ability to precisely measure BH masses in active galaxies, which will enable more confident probes of accretion physics for the most massive galaxies.