  If G is a finite connected graph, then an arithmetical structure on $G$ is a
pair of vectors $(\mathbf{d}, \mathbf{r})$ with positive integer entries such
that $(\diag(\mathbf{d}) - A)\cdot \mathbf{r} = \mathbf{0}$, where $A$ is the
adjacency matrix of $G$ and the entries of $\mathbf{r}$ have no common factor
other than $1$. In this paper, we generalize the result of Archer, Bishop,
Diaz-Lopez, Garc\'ia Puente, Glass, and Louwsma on enumerating arithmetical
structures on bidents (also called coconut tree graphs $\CT{p}{2}$) to all
coconut tree graphs $\CT{p}{s}$ which consists of a path on $p>0$ vertices to
which we append $s>0$ leaves to the right most vertex on the path. We also give
a characterization of smooth arithmetical structures on coconut trees when
given number assignments to the leaf nodes.
