We report measurements of the branching fractions and $CP$ asymmetries for $D_s^{+} rightarrow K^{+} eta $, $D_s^{+} rightarrow K^{+} pi^0 $, and $D_s^{+} rightarrow pi^{+} eta $ decays, and the branching fraction for $D_s^{+} rightarrow pi^{+} pi^0$. Our results are based on a data sample corresponding to an integrated luminosity of 921 fb$^{-1}$ collected by the Belle detector at the KEKB $e^+e^-$ asymmetric-energy collider. Our measurements of $CP$ asymmetries in these decays are the most precise to-date; no evidence for $CP$ violation is found.