The crucial role played by social interactions between smart objects in the Internet of Things is being rapidly recognized by the Social Internet of Things (SIoT) vision. In this paper, we build upon the recently introduced vision of Speaking Objects – “things” interacting through argumentation – to show how different forms of human dialogue naturally fit cooperation and coordination requirements of the SIoT. In particular, we show how speaking objects can exchange arguments in order to seek for information, negotiate over an issue, persuade others, deliberate actions, and so on, namely, striving to reach consensus about the state of affairs and their goals. In this context, we illustrate how argumentation naturally enables such a form of conversational coordination through practical examples and a case study scenario.