  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 about 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) x 10^8 Msun, assuming that we have accurately subtracted the AGN
and starburst light contributions, which have a luminosity of about 10^9 Lsun;
(3) The SMBH mass agrees with the SMBH-stellar mass relation but is about 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 Msun/yr. 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.
