  Production of $c\bar c$ pairs in elementary hadron-hadron collisions is
introduced in a simulation of relativistic heavy ion collisions. Coalescence of
charmed quarks and antiquarks into various charmonium states is performed and
the results are compared to PHENIX J$/\psi$ Au+Au data. The $\chi$ and $\psi$'
bound states must be included as well as the ground state J$/\psi$, given the
appreciable feeding from the excited states down to the J$/\psi$ via gamma
decays. Charmonium coalescence is found to take place at relatively late times:
generally after $c$($\bar c$)-medium interactions have ceased. Direct
production of charmonia through hadron-hadron interactions, {\it ie.} without
explicit presence of charm quarks, occurring only at early times, is suppressed
by collisions with comoving particles and accounts for some $\sim 5\%$ of the
total J$/\psi$ production. Coalescence is especially sensitive to the level of
open charm production, scaling naively as $n_{c\bar c}^2$. The J$/\psi$
transverse momentum distribution is dependent on the charm quark transverse
momentum distribution and early charm quark-medium interaction, thus providing
a glimpse of the initial collision history.
