The CMS detector at the LHC is well suited for the study of quarkonium states J/ , ¢ ¡ % for J/ . The precise tracker enables dimuon reconstruction with efficiencies above 90% in the barrel for dimuons from quarkonia decays, a dimuon mass resolution of 0.5% at the £ mass, and background rejection. Results of quarkonium simulations are presented for several ion species with high and low background hypotheses. The expected dimuon invariant mass distributions are shown and the signalto-background ratios, significance and the estimated statistics are also given. The CMS capability for detecting high-mass pairs from semileptonic decays and secondary J/ 's from single B decays (useful channels for studying medium-induced bottom-quark energy loss) is also discussed.