In this paper we consider the problem of allowing a humanoid robot that is subject to a persistent disturbance, in the form of a payload-carrying task, to follow given planned footsteps. To solve this problem, we combine an online nonlinear centroidal Model Predictive Controller - MPC with a contact stable force parametrization. The cost function of the MPC is augmented with terms handling the disturbance and regularizing the parameter. The performance of the resulting controller is validated both in simulations and on the humanoid robot iCub. Finally, the effect of using the parametrization on the computational time of the controller is briefly studied.