This technical note addresses the cooperative global output regulation problem for second-order nonlinear multi-agent systems without a priori knowledge of the control direction. We will propose both the graph-dependent and graph-independent distributed controllers based on the combination of the internal model, the Nussbaum-type dynamic gain, and the adaptive control technique. Comparing with some existing results, our novel design can handle the multi-agent system with not only the arbitrary and non-identical unknown control direction but also the uncertain parameter that belongs to any unknown and non-compact set.