This paper discusses the manipulation of an object under equilibrium where the object makes rolling contact with the plate attached at the tip of the arm. We assume that the object satisfies the neighborhood equilibrium [1], where an object with rolling contact can automatically find another equilibrium state close to the original one even when the current one is broken due to the change of input. For always guaranteeing the neighborhood equilibrium, we newly define the contact stable region on the object surface. By utilizing the contact stable region, we propose a control scheme for manipulating an object from one to the desired position on a plate whose posture is controllable. Numerical example is also shown to explain our idea.