Star-forming galaxies (SFGs) with stellar masses below 1010 M⊙ make up the bulk of the galaxy population at z > 2. The properties of the cold gas in these galaxies can only be probed in very deep observations or by targeting strongly lensed galaxies. Here we report the results of a pilot survey using the Atacama Compact Array of molecular gas in the most strongly magnified galaxies selected as giant arcs in optical data. The selection in rest-frame ultraviolet (UV) wavelengths ensures that sources are regular SFGs, without a priori indications of intense dusty starburst activity. We conducted Band 4 and Band 7 observations to detect mid-J CO, [C » I] and thermal continuum as molecular gas tracers from four strongly lensed systems at z ≈ 2 - 3: our targets are SGAS J1226651.3+215220 (A and B), SGAS J003341.5+024217 and the Sunburst Arc. The measured molecular mass was then projected onto the source plane with detailed lens models developed from high resolution Hubble Space Telescope observations. Multiwavelength photometry was then used to obtain the intrinsic stellar mass and star formation rate via spectral energy distribution modeling. In only one of the sources are the three tracers robustly detected, while in the others they are either undetected or detected in continuum only. The implied molecular gass masses range from 4 × 109 M⊙ in the detected source to an upper limit of ≲ 109 M⊙ in the most magnified source. The inferred gas fraction and gas depletion timescale are found to lie approximately 0.5-1.0 dex below the established scaling relations based on previous studies of unlensed massive galaxies, but in relative agreement with existing literature about UV-bright lensed galaxies at these high redshifts. Our results indicate that the cold gas content of intermediate to low mass galaxies should not be extrapolated from the trends seen in more massive high-z galaxies. The apparent gas deficit is robust against biases in the stellar mass or star formation rate. However, we find that in this mass-metallicity range, the molecular gas mass measurements are severely limited by uncertainties in the current tracer-to-gas calibrations.