Using data collected near the Ds*+ Ds- peak production energy Ecm = 4170 MeV by the CLEO-c detector, we study the decays of Ds+ mesons to two pseudoscalar mesons. We report on searches for the singly-Cabibbo-suppressed Ds+ decay modes K+ eta, K+ eta, pi+ K0S, K+ pi0, and the isospin-forbidden decay mode Ds+ to pi+ pi0. We normalize with respect to the Cabibbo-favored Ds+ modes pi+ eta, pi+ eta, and K+ K0S, and obtain ratios of branching fractions: Ds+ to K+ eta / Ds+ to pi+ eta = (8.9 +- 1.5 +- 0.4)%, Ds+ to K+ eta / Ds+ to pi+ eta = (4.2 +- 1.3 +- 0.3)%, Ds+ to pi+ K0S / Ds+ to K+ K0S = (8.2 +- 0.9 +- 0.2)%, Ds+ to K+ pi0 / Ds+ to K+ K0S = (5.0 +- 1.2 +- 0.6)%, and Ds+ to pi+ pi0 / Ds+ to K+ K0S < 4.1% at 90% CL, where the uncertainties are statistical and systematic, respectively.