A

Step 1: When the magnet oscillates, it creates a changing magnetic field in the vicinity of the coil, according to Faraday's law of electromagnetic induction.
Step 2: As the magnet moves in and out of the coil, it induces an alternating current in the coil.
Step 3: This alternating current results in a deflection in the galvanometer to the left when the current flows in one direction and to the right when the current flows in the opposite direction.
Step 4: Since the oscillation of the magnet is periodic, the amplitude of deflection remains constant as long as the oscillation's energy is preserved.
Therefore, the correct answer is A: 'G shows deflection to the left and right with constant amplitude.'