  We study the elliptic and triangular flow of charmonium states, or $J/\psi$,
$\psi(2S)$, and $\chi_c(1P)$ mesons in heavy ion collisions. Starting from the
evaluation of charmonia transverse momentum distributions and yields, we
calculate elliptic and triangular flow of charmonium states based on the
coalescence model. We show that the internal structure, or the wave function
distribution of charmonium states plays a significant role, especially when
charmonium states are produced by charm quark recombination, leading to the
transverse momentum distribution of the $\psi(2S)$ meson as half large as that
of the $J/\psi$ meson. We also consider the dependence of the elliptic and
triangular flow of charmonium states on internal structures of charmonium
states, and find that the wave function effects as well as feed-down
contributions are averaged out for elliptic and triangular flow, resulting in
similar elliptic and triangular flow for all charmonium states. We investigate
further the elliptic and triangular flow of charmonium states at low transverse
momentum region, and also discuss the quark number scaling of elliptic and
triangular flow for charmonium states.
