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 B(B^+ -> J/psi K^+) to derive
B(B^+ -> psi(2S) K^+) = (0.56 +/- 0.08 +/- 0.10) x 10^-3, B(B^0 -> psi(2S)
K^*(892)^0) = (0.92 +/- 0.20 +/- 0.16) x 10^-3, and B(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.