A numerical technique is developed for searching for the stability boundary for a resistive, straight-cylinder, magnetohydrodynamic equilibrium with spatially-dependent resistivity. For fixed aspect ratio, the boundary is a curve in the plane whose axes are Hartmann number and pinch ratio (or reciprocal of the safety factor at the wall). The technique is spectral and utilizes orthonormal eigenfunctions of the curl. Nonlinear behavior above the stability boundary is computed for a particular profile, using a nonlinear version of the code.