  We report the observations of the decays B^+ -> psi(2S) K^+ and B^0 ->
psi(2S) K^*(892)^0 in ppbar collisions at a center-of-mass energy of 1.8 TeV
using a 110 pb^{-1} data sample recorded by the Collider Detector at Fermilab.
We also reconstruct the decays B^+ -> J/psi K^+ and B^0 -> J/psi K^*(892)^0 and
measure the six ratios of branching fractions of these four decays. The
relative branching-fraction results are shown to be consistent with
phenomenological factorization calculations of hadronic B-meson decays. We use
the world-average branching fraction Br(B^+ -> J/psi K^+) to derive Br(B^+ ->
psi(2S) K^+) = (0.56 +/- 0.08 +/- 0.10) x 10^{-3}, Br(B^0 -> psi(2S)
K^*(892)^0) = (0.92 +/- 0.20 +/- 0.16) x 10^{-3}, and Br(B^0 -> J/psi
K^*(892)^0) = (1.78 +/- 0.14 +/- 0.29) x 10^{-3}, where the first and second
uncertainties are statistical and systematic, respectively.
