  We propose the use of a superconducting charge qubit capacitively coupled to
two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e.
quantum superpositions of pairs of distinguishable coherent states 180$^\circ$
out of phase with each other. This is achieved by effectively implementing Kerr
nonlinearities induced through application of a strong external driving field
in one of the resonators. A simple study of the effect of dissipation on our
scheme is also presented, and lower bounds of fidelity and purity of the
generated state are calculated. Our procedure to implement a Kerr nonlinearity
in this system may be used for high precision measurements in nanomechanical
resonators.
