Through what procedure is canon law amended?
Popes promulgate new Codes of Canon Law at their own discretion.
During the course of the centuries the Catholic Church has been accustomed to reform and renew the laws of canonical discipline so that in constant fidelity to its divine founder, they may be better adapted to the saving mission entrusted to it. Prompted by this same purpose and fulfilling at last the expectations of the whole Catholic world, I order today, January 25, 1983, the promulgation of the revised Code of Canon Law. In so doing, my thoughts go back to the same day of the year 1959 when my predecessor of happy memory, John XXIII, announced for the first time his decision to reform the existing corpus of canonical legislation which had been promulgated on the feast of Pentecost in the year 1917. Code of Canon Law (1983)
The pope has ultimate and immediate jurisdiction within the Catholic Church. As such, he can amend or create a new version of canon law at will, but would most certainly be done with a number of Vatican canonists and officials helping out.
Papal supremacy is the doctrine of the Roman Catholic Church that the Pope, by reason of his office as Vicar of Christ and as the visible foundation and source of unity, and as pastor of the entire Christian Church, has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered: that, in brief, "the Pope enjoys, by divine institution, supreme, full, immediate, and universal power in the care of souls." - Papal supremacy (Wikipedia)
Or if you prefer something from Catechism of the Catholic Church:
882 The Pope, Bishop of Rome and Peter's successor, "is the perpetual and visible source and foundation of the unity both of the bishops and of the whole company of the faithful. For the Roman Pontiff, by reason of his office as Vicar of Christ, and as pastor of the entire Church has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered."
937 The Pope enjoys, by divine institution, "supreme, full, immediate, and universal power in the care of souls".
Thus a pope can change, amend or create another code of canon law as he deems necessary for the sake of the Church. It would certainly always be done with the collaborations of various theologians, canonists and Vatican officials. Although it is true that the pope could do so on his own, reason dictates that he would always take council in doing so.
When St. John Paul promulgated the new law, the pope said, he wrote that it was the result of an effort "to translate into canonical language ... the conciliar ecclesiology," that is, the Second Vatican Council's vision of the church, its structure and relation to its members and the world. - Pope Francis: Canon law must serve Vatican II vision of the Church
Every once and awhile canon law is amended or updated as I like to say as the following posts bare out:
Another way is open for amending canon law. This occurs when a group (usually bishops) put forth a dubium (doubt) about a particular clause or phrase within Canon Law. When Pope St. John Paul II first promulgated the 1983 Code of Canon Law, it received at least one dubium almost from it very promulgation: Communion - How many times per day?