  Let $G$ be a graph with no isolated vertices. A {\em $k$-coupon coloring} of
$G$ is an assignment of colors from $[k] := \{1,2,\dots,k\}$ to the vertices of
$G$ such that the neighborhood of every vertex of $G$ contains vertices of all
colors from $[k]$. The maximum $k$ for which a $k$-coupon coloring exists is
called the {\em coupon coloring number} of $G$, and is denoted $\chi_{c}(G)$.
In this paper, we prove that every $d$-regular graph $G$ has $\chi_{c}(G) \geq
(1 - o(1))d/\log d$ as $d \rightarrow \infty$, and the proportion of
$d$-regular graphs $G$ for which $\chi_c(G) \leq (1 + o(1))d/\log d$ tends to
$1$ as $|V(G)| \rightarrow \infty$.
