  We study polynomial deformations of the fuzzy sphere, specifically given by
the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the
Poisson structure on a surface in $\mathbb{R}^3$. We find that several
surfaces, differing by constants, are described by the Higgs algebra at the
fuzzy level. Some of these surfaces have a singularity and we overcome this by
quantizing this manifold using coherent states for this nonlinear algebra. This
is seen in the measure constructed from these coherent states. We also find the
star product for this non-commutative algebra as a first step in constructing
field theories on such fuzzy spaces.
