Two new methods for designing modular stellarator coils are presented. Stellarator coils provide necessary magnetic field to produce the plasma shape for a desired magnetohydrodynamic (MHD) equilibrium. The methods optimize a continuous current on a surface - i.e., coil current is represented by a continuous-current sheet on a toroidal winding surface - and the process of coil cutting is not addressed. In contrast to previously published continuous-current methods that optimize coil current by minimizing the flux at the plasma boundary, the new methods presented in this paper search for optimal solutions by minimizing the displacement of the plasma boundary, i.e., the last closed magnetic surface. The physical displacement of the plasma boundary is computed from the magnetic field normal using linear MHD perturbation theory. A comparison with two similar continuous-current codes is given in terms of both methodology and results. The new codes show modest improvement over previously published continuous-current codes.