In sustainable farming, the use of organic fertilizers is a costly but environmentally-oriented type of soil–crop system management. Among essential microelements, cobalt (Co) deficiency commonly occurs in arid and semi-arid climatic regions suitable for the growing of moringa (Moringa oleifera Lam), an economically important, multipurpose tree. Therefore, in this study, two pot experiments were conducted to identify the interaction effects of Co and organic fertilizers in modifying the growth, yield, and nutritional composition of moringa. Each experiment consisted of 21 treatments as combinations of seven concentrations of Co (0.0, 2.5, 5.0, 7.5, 10.0, 12.5, and 15.0 mg L−1) and three organic fertilizers (chicken manure, CM; farmyard manure, FYM; and compost, Comp). Co, at 7.5–12.5 mg L−1, in combination with CM, significantly increased the height, leaf number, leaf area, and dry weight of plants, as well as N, P, K, Zn, Cu, protein, total carbohydrate, total soluble solids, total phenolics, carotenoids, and vitamin C in leaves. Co was positively correlated with N, P, K, and the dry weight content in moringa leaves, and this synergistic interaction may underpin the remaining parameters enhanced by Co. The cobalt effect was dose-dependent, so the improved growth, yield, and nutritional composition of moringa can be managed through a proper Co dose in combination with organic fertilizer. Co and organic fertilization could be a promising strategy for improving moringa plant productivity and its biological value in conditions of sandy soils and Co deficiency.