  The galaxy cluster Zwicky 3146 is a sloshing cool core cluster at $z=0.291$
that in X-ray imaging does not appear to exhibit significant pressure
substructure in the intracluster medium (ICM). The published $M_{500}$ values
range between $3.88^{+0.62}_{-0.58}$ to $22.50 \pm 7.58 \times 10^{14}$
M$_{\odot}$, where ICM-based estimates with reported errors $<20$\% suggest
that we should expect to find a mass between $6.53^{+0.44}_{-0.44} \times
10^{14}$ M$_{\odot}$ (from Planck, with an $8.4\sigma$ detection) and
$8.52^{+1.77}_{-1.47} \times 10^{14}$ M$_{\odot}$ (from ACT, with a $14\sigma$
detection). This broad range of masses is suggestive that there is ample room
for improvement for all methods. Here, we investigate the ability to estimate
the mass of Zwicky 3146 via the Sunyaev-Zel'dovich (SZ) effect with data taken
at 90 GHz by MUSTANG-2 to a noise level better than $15\ \mu$K at the center,
and a cluster detection of $104\sigma$. We derive a pressure profile from our
SZ data which is in excellent agreement with that derived from X-ray data. From
our SZ-derived pressure profiles, we infer $M_{500}$ and $M_{2500}$ via three
methods -- $Y$-$M$ scaling relations, the virial theorem, and hydrostatic
equilibrium -- where we employ X-ray constraints from \emph{XMM-Newton} on the
electron density profile when assuming hydrostatic equilibrium. Depending on
the model and estimation method, our $M_{500}$ estimates range from $6.23 \pm
0.59$ to $10.6 \pm 0.95 \times 10^{14}$ M$_{\odot}$, where our estimate from
hydrostatic equilibrium, is $8.29^{+1.93}_{-1.24}$ ($\pm 19.1$\% stat)
${}^{+0.74}_{-0.68}$ ($\pm 8.6$\% sys, calibration) $\times 10^{14}$
M$_{\odot}$. Our fiducial mass, derived from a $Y$-$M$ relation is
$8.16^{+0.44}_{-0.54}$ ($\pm 5.5$\% stat) ${}^{+0.46}_{-0.43}$ ($\pm 5.5$\%
sys, $Y$-$M$) ${}^{+0.59}_{-0.55}$ ($\pm 7.0$\% sys, cal.) $\times 10^{14}$
M$_{\odot}$.
