We report on the reconstruction of the decay mode B^0 -> J/psi
K^0_s using 19.3 pb^-1 of data collected by the Collider Detector at Fermilab
in pbar p collisions at sqrt s = 1.8 TeV.  A signal of 41.8 +/- 6.9 events,
with a signal-to-background ratio of 9:1, is observed.  Three additional decay
modes B^+ -> J/psi K^+, B^0 -> J/psi K^*(892)^0 and B^+ -> J/psi K^*(892)^+
are reconstructed.  We measure three ratios of branching ratios, each one
relative to the B^+ -> J/psi K^+ mode.  We also report the ratio of production
rates, Gamma(B -> J/psi K^*)/Gamma(B -> J/psi K), for the vector-vector
relative to the vector-pseudoscaler modes, to be 1.32 +/- 0.23(stat.) +/- 0.16
(syst.).