First observations of the B-S(0) ->psi(2S)eta, B-(s)(0) ->psi(2S)pi(+)pi(-) decays are made using a dataset corresponding to an integrated luminosity of 1.0 fb(-1) collected by the LHCb experiment in proton proton collisions at a centre-of-mass energy of root s = 7 TeV. The ratios of the branching fractions of each of the (2S) modes with respect to the corresponding J/psi decays are B(B-s(0) ->psi(2S)eta)/B(B-s(0) -> J(2S)eta) = 0.83 +/- 0.14 (stat) +/- 0.12 (B), B(B0 ->psi(2S)pi(+)pi(-))/B(B0 -> J/psi pi(+)pi(-)) = 0.56 +/- 0.07 (stat) +/- 0.05 (syst) +/- 0.01 (B), B(B0 ->psi(2S)pi(+)pi(-))/B(B-s(0) -> J/psi pi(+)pi(-)) = 0.34 +/- 0.04 (stat) +/- 0.03 (syst) +/- 0.01 (B). where the third uncertainty corresponds to the uncertainties of the dilepton branching fractions of the J/ and psi(28) meson decays. (C) 2013 CERN. Published by Elsevier BA/. All rights reserved.