This study examined the relationships among supervisors' coaching leadership, AI literacy, AI-contextualized perceived organizational support (AI-POS), and employees' innovative behavior in South Korean small and medium-sized enterprises (SMEs). Using PLS-SEM with data from 429 employees, coaching leadership showed a strong association with AI literacy (β = .397, p < .001), while its direct association with innovative behavior was modest (β = .096, p = .047). Approximately 72.9% of the total effect of coaching leadership on innovative behavior was transmitted indirectly through AI literacy (indirect effect β = .258), indicating that coaching leadership functions primarily as an enabler of AI competency development rather than a direct driver of innovation. AI literacy exhibited the strongest association with innovative behavior (β = .649, p < .001). CFA results revealed that the instrumental and psychological support dimensions of AI-POS were empirically non-separable (inter-factor correlation = 1.000), and a unified AI-POS composite was therefore adopted as the primary moderator. AI-POS significantly moderated the AI literacy–innovative behavior relationship (β = .181, p < .001), suggesting that organizational AI support strengthens the conversion of AI competency into innovative behavior. Sub-dimension analyses were treated as exploratory given extreme inter-correlations among coaching leadership sub-dimensions (r = .929–.940, VIF > 10). These findings extend coaching leadership theory and the AMO framework to the AI context.