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 ($D=15.8pm0.4$ 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 $0.25times10^7,M_odot lesssim M_mathrm{BH} lesssim 3times10^7,M_odot$. 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.
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