  The mass of a supermassive black hole ($M_\mathrm{BH}$) is a fundamental
property that can be obtained through observational methods. Constraining
$M_\mathrm{BH}$ through multiple methods for an individual galaxy is important
for verifying the accuracy of different techniques, and for investigating the
assumptions inherent in each method. NGC 4151 is one of those rare galaxies for
which multiple methods can be used: stellar and gas dynamical modeling because
of its proximity ($D=15.8\pm0.4$ Mpc from Cepheids), and reverberation mapping
because of its active accretion. In this work, we re-analyzed $H-$band integral
field spectroscopy of the nucleus of NGC 4151 from Gemini NIFS, improving the
analysis at several key steps. We then constructed a wide range of axisymmetric
dynamical models with the new orbit-superposition code Forstand. One of our
primary goals is to quantify the systematic uncertainties in $M_\mathrm{BH}$
arising from different combinations of the deprojected density profile,
inclination, intrinsic flattening, and mass-to-light ratio. As a consequence of
uncertainties on the stellar luminosity profile arising from the presence of
the AGN, our constraints on \mbh are rather weak. Models with a steep central
cusp are consistent with no black hole; however, in models with more moderate
cusps, the black hole mass lies within the range of $0.25\times10^7\,M_\odot
\lesssim M_\mathrm{BH} \lesssim 3\times10^7\,M_\odot$. This measurement is
somewhat smaller than the earlier analysis presented by Onken et al., but
agrees with previous $M_\mathrm{BH}$ values from gas dynamical modeling and
reverberation mapping. Future dynamical modeling of reverberation data, as well
as IFU observations with JWST, will aid in further constraining $M_\mathrm{BH}$
in NGC 4151.
