Using a sample of 3.08x10(6) psi(2S) decays collected at root s=3.686 GeV with the CLEO detector at the Cornell Electron Storage Ring, we have measured the branching fractions for psi(2S) decays to pseudoscalar pairs pi(+)pi(-), K+K- and (KSKL0)-K-0. We obtain B(psi(2S)->pi(+)pi(-))< 2.1x10(-5) (90% C.L.), B(psi(2S)-> K+K-)=(6.3 +/- 0.6(stat)+/- 0.3(syst))x10(-5), and B(psi(2S)->(KSKL0)-K-0)=(5.8 +/- 0.8(stat)+/- 0.4(syst))x10(-5). The branching fractions allow extraction of the relative phase Delta=(95 +/- 15)degrees and strength ratio R=(2.5 +/- 0.4) of the three-gluon and one-photon amplitudes for these modes.