  The contribution of J/\psi production from coherent and incoherent
photon-induced production is calculated in Au+Au and Cu+Cu collisions at
$\sqrt{s_{NN}} = 200$ GeV. The yield and nuclear modification factors
($R_{AA}$) contributed by photoproduction are presented as functions of
transverse momentum ($p_T$) and centrality at both mid- and forward rapidity.
The $R_{AA}$ of J/\psi from photoproduction is found to be as high as 0.6 in
the lowest $p_{T}$ bin ($0 < p_{T} < 1$ GeV/$c$) at mid-rapidity in 60-92\%
Au+Au collisions. The $R_{AA}$ measured in Au+Au and Cu+Cu collisions at
$\sqrt{s_{NN}} = 200$ GeV are corrected by subtracting the calculated
photoproduction contribution.
