  In this paper we consider groups of the form $G\wr L$, where the set of
generators naturally extends the sets of generators of $G$ and $L$, and $L$
admits a Cayley graph that is a tree. We show how one can compute the conjugacy
growth series of such groups in terms of the standard and conjugacy growth
series of $G$. We then provide explicit formulas for groups of the form $G\wr
\mathbb{Z}$ and $G\wr (C_2*C_2)$.
  We also prove that the radius of convergence of the conjugacy growth series
of $G\wr L$, for any $G$ and $L$ as above, is the same as the radius of
convergence of its standard growth series.
