The mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) is probing supermassive black holes (SMBHs) in galaxies across the Hubble sequence via molecular gas dynamics. We present the first WISDOM study of a luminous infrared galaxy with an active galactic nuclei (AGN): Fairall 49. We use new ALMA observations of the CO(2 − 1) line with a spatial resolution of ∼ 80 pc together with ancillary HST imaging. We reach the following results: (1) The CO kinematics are well described by a regularly rotating gas disk with a radial inflow motion, suggesting weak feedback on the cold gas from both AGN and starburst activity; (2) The dynamically inferred SMBH mass is 1 . 6 ± 0 . 4 ( rnd ) ± 0 . 8 ( sys ) × 10 8 M (cid:12) assuming that we have accurately subtracted the AGN and starburst light contributions, which have a luminosity of ∼ 10 9 L (cid:12) ; (3) The SMBH mass agrees with the SMBH − stellar mass relation but is ∼ 50 times higher than previous estimates from X-ray variability; (4) The dynamically inferred molecular gas mass is 30 times smaller than that inferred from adopting the Galactic CO-to-H 2 conversion factor ( 𝑋 CO ) for thermalised gas, suggesting low values of 𝑋 CO ; (5) the molecular gas inflow rate increases steadily with radius and may be as high as ∼ 5 𝑀 (cid:12) yr − 1 . This work highlights the potential of using high-resolution CO data to estimate, in addition to SMBH masses, the X CO factor and gas inflow rates in nearby galaxies.