Solution-processable semiconductors with antiferromagnetic (AFM) order are attractive for future spintronics and information storage technology. Halide perovskites containing magnetic ions have emerged as multifunctional materials, demonstrating a cross-link between structural, optical, electrical, and magnetic properties. However, stable optoelectronic halide perovskites that are antiferromagnetic remain sparse, and the critical design rules to optimize magnetic coupling still must be developed. Here, we combine the complementary magnetometry and electron-spin-resonance experiments, together with first-principles calculations to study the antiferromagnetic coupling in stable Cs-2(Ag:Na)FeCl6 bulk semiconductor alloys grown by the hydrothermal method. We show the importance of nonmagnetic monovalence ions at the B-I site (Na/Ag) in facilitating the superexchange interaction via orbital hybridization, offering the tunability of the Curie-Weiss parameters between -27 and -210 K, with a potential to promote magnetic frustration via alloying the nonmagnetic B-I site (Ag:Na ratio). Combining our experimental evidence with first-principles calculations, we draw a cohesive picture of the material design for B-site-ordered antiferromagnetic halide double perovskites.