The effects of partial coherence on the propagation of dispersive Alfvén waves in a magnetoplasma are investigated. In particular, nonlinear interactions between dispersive Alfvén waves and ion-acoustic perturbations are considered by means of a Wigner formalism. A set of governing equations consisting of a kinetic equation for dispersive Alfvén waves coupled nonlinearly to a ponderomotive force driven ion-acoustic wave equation is obtained. The governing nonlinear equations are used to derive a nonlinear dispersion relation that is appropriate for investigating the modulational instability of broadband Alfvén wavepackets. The spectral broadening of the Alfvén waves gives rise to new regimes for the growth rate of the modulational instability.