Genistein, an isoflavone known for its antioxidant and antidiabetic effects, suffers from the drawback of low solubility. To overcome this limitation, co-amorphous systems were synthesized by incorporating amino acids that were chosen through computational methods. The confirmation of the amorphous state of lysine and arginine-containing systems was ascertained by X-ray powder diffraction. Subsequently, the characterization of these systems was extended by employing thermo-gravimetry, differential scanning calorimetry, Fourier-transform infrared spectroscopy, and scanning electron microscopy. The investigation also included an assessment of the physical stability of the samples during storage. The apparent solubility of the systems was studied in an aqueous medium. To evaluate the in vitro permeability through the gastrointestinal tract, the parallel artificial membrane permeability assay was employed. The biological properties of the systems were assessed with regard to their antioxidant activity using 2,2-diphenyl-1-picrylhydrazyl and cupric ion-reducing antioxidant capacity assays, as well as their ability to inhibit α-glucosidase. The systems’ glass transition temperatures were determined, and their homogeneity confirmed via differential scanning calorimetry analysis, while Fourier-transform infrared spectroscopy analysis provided data on molecular interactions. Stability was maintained for the entire 6-month storage duration. The co-amorphous system containing lysine displayed the most pronounced apparent solubility improvement, as well as a significant enhancement in antioxidant activity. Notably, both systems demonstrated superior α-glucosidase inhibition relative to acarbose, a standard drug for managing type 2 diabetes. The results indicate that co-amorphous systems with lysine and arginine have the potential to significantly enhance the solubility and biological activity of genistein.