  The yield of $J/\psi$ mesons, produced in proton-nucleus ($p+A$) and
nucleus-nucleus ($A+A$) collisions are estimated within a Glauber model ansatz
for the upcoming low energy heavy-ion collision experiments at SPS and FAIR. A
data driven parametrization is employed to incorporate the effects of Cold
Nuclear Matter (CNM) on the $J/\psi$ production cross-section.
