The XRISM Resolve microcalorimeter array measured the velocities of hot intracluster gas at two positions in the Coma galaxy cluster: 3 ′ × 3 ′ squares at the center and at 6 ′ (170 kpc) to the south. We find the line-of-sight velocity dispersions in those regions to be σ _z = 208 ± 12 km s ⁻¹ and 202 ± 24 km s ⁻¹ , respectively. The central value corresponds to a 3D Mach number of M = 0.24 ± 0.015 and a ratio of the kinetic pressure of small-scale motions to thermal pressure in the intracluster plasma of only 3.1% ± 0.4%, at the lower end of predictions from cosmological simulations for merging clusters like Coma, and similar to that observed in the cool core of the relaxed cluster A2029. Meanwhile, the gas in both regions exhibits high line-of-sight velocity differences from the mean velocity of the cluster galaxies, Δ v _z = 450 ± 15 km s ⁻¹ and 730 ± 30 km s ⁻¹ , respectively. A small contribution from an additional gas velocity component, consistent with the cluster optical mean, is detected along a sight line near the cluster center. The combination of the observed velocity dispersions and bulk velocities is not described by a Kolmogorov velocity power spectrum of steady-state turbulence; instead, the data imply a much steeper effective slope (i.e., relatively more power at larger linear scales). This may indicate either a very large dissipation scale, resulting in the suppression of small-scale motions, or a transient dynamic state of the cluster, where large-scale gas flows generated by an ongoing merger have not yet cascaded down to small scales.