  In this paper we describe conjugacy geodesic representatives in any dihedral
Artin group $G(m)$, $m\geq 3$, which we then use to calculate asymptotics for
the conjugacy growth of $G(m)$, and show that the conjugacy growth series of
$G(m)$ with respect to the `free product' generating set $\{x, y\}$ is
transcendental. We prove two additional properties of $G(m)$ that connect to
conjugacy, namely that the permutation conjugator length function is constant,
and that the falsification by fellow traveler property (FFTP) holds with
respect to $\{x, y\}$. These imply that the language of all conjugacy geodesics
in $G(m)$ with respect to $\{x, y\}$ is regular.
