We investigate the effect of ion-specific potentials on the force between a nanoprobe attached to a cantilever tip, and a charged surface. The probe is treated as a spherical nanoparticle with constant charge. A modified Poisson-Boltzmann equation in bispherical coordinates is used to address this problem in a more quantitative way. We predict that the ion-specific series of measured forces depend on the sign and magnitude of surface charge densities.