We propose the first class of simultaneous voting mechanisms in which each Nash equilibrium is coalition-proof. These mechanisms hence prevent the coordination failures which arise when some (coalition of) voters could have induced an outcome that they all prefer to the equilibrium outcome had they agreed on a common strategy. In each of these mechanisms, some voter(s) has the right to veto a list of alternatives. For each specification of the veto rights, each of these mechanisms implements a Veto by random priority rule introduced by Moulin [1981]. We then discuss necessary conditions for arbitrary mechanisms to implement a Pareto efficient rule ensuring that each equilibrium is coalition-proof. We show that the presence of veto rights in the mechanism is unavoidable to achieve this demanding implementation notion.