What is the ruling on committing this sin with one's wife, and is repentance from it permissible, and what is the method for such repentance?

The questioner did not clarify the nature of the sin to explain its ruling. However, Allah accepts the repentance of His servant and rejoices in it, no matter what the sin, as stated in His Almighty saying: "And He it is Who accepts repentance from His servants and pardons sins" and "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah.'" The spouses must offer sincere repentance, fulfilling its conditions, which are remorse and cessation of the disobedience, and increasing their acts of seeking forgiveness and obedience.