I 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, I calculate elliptic and triangular flow of charmonium states based on the coalescence model. I 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. I 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. I 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.