We observed a sample of three Brightest Cluster Galaxies (BCGs), Abell 1836-BCG, Abell 2052-BCG, and Abell 3565-BCG, with the Advanced Camera for Surveys (ACS) and the Imaging Spectrograph (STIS) on board the Space Telescope. For each target galaxy we obtained high-resolution spectroscopy of the Hα and [N II] λ6583 emission lines at three slit positions, to measure the central ionized-gas kinematics. ACS images in three different filters (F435W, F625W, and FR656N) have been used to determine the optical depth of the dust, stellar mass distribution near the nucleus, and intensity map. We present supermassive black hole (SBH) mass estimates for two galaxies which show regular rotation curves and strong central velocity gradients, and an upper limit on the SBH mass of the third one. For the SBHs of Abell 1836-BCG and Abell 3565-BCG, we derived M• = 4.8+0.8−0.7 × 109 M⊙ and M• = 1.3+0.3−0.4 × 109 M⊙ at 1 σ confidence level, respectively. For the SBH of Abell 2052-BCG, we found M• ≤ 7.3 × 109 M⊙.