Theoretically, a penny will be more massive when it has a negative charge than when it has a positive charge.
Work Step by Step
When a penny loses electrons, it acquires a positive charge. Theoretically speaking, its mass decreases, by the mass of the electrons that went away. Practically speaking, this mass loss is far, far, far too small to measure for a penny. A similar argument shows that when an object gains electrons, it acquires a negative charge. Theoretically speaking, its mass increases, by the mass of the electrons that it picked up.