The dynamics of coupled ion-acoustic waves is investigated in an electronegative plasma made of Boltzmann negative ions, cold mobile positive ions and Boltzmann electrons. Using the reductive perturbation method, it is shown that the system can fully be described by a set of two coupled nonlinear Schrödinger equations. The parametric analysis of modulational instability reveals the existence of regions of instability that are sensitive to changes in plasma parameters such as the negative ion concentration ratio and the electron-to-negative ion temperature ratio. The analytical results are confronted to numerical simulations, where we examine the long-time dynamics of modulated waves in the electronegative plasma. One obtains the generation of nonlinear modulated waves that are sensitive to the negative-ion concentration ratio. Exact solutions for individual modes are discussed and one finally derives the coupled solution. The response of the latter to the plasma parameter variations is also addressed.