In the field of metamaterial design, tailoring nonlinearities can markedly expand the realm of wave manipulations. However, the optimal design of metamaterials with nonlinearities is hampered by a dynamic behavior that exhibits discontinuities and is highly sensitive to uncertainties. For this reason, a specific stochastic design optimization approach is introduced. The algorithm tackles discontinuities and accounts for uncertainties. In addition, the approach introduces a formulation based on a field representation of the design variables, thus reducing the dimensionality of the problem. The stochastic optimization algorithm is demonstrated on the vibration mitigation of a chain of nonlinear resonators. It is shown that the combination of the stochastic optimization algorithm and field representation provides more flexibility in tailoring the chain properties.