New custodes can certainly be created, they are chosen from sons of noble houses and the process of their recruitment and creation is not known to anybody outside those creating them.
We know for certain that new Custodes are created after the Horus Heresy. From the Lexicanum Article on the Adeptus Custodes:
Although the Legio Custodes originally numbered ten thousand, around five years into the War Within the Webway they had been reduced to around a thousand. However, by the 41st Millennium, they had rebuilt to their original 10,000 strength.
So, they still know how to create a new Custodes, although it is not known how they are created. From the Codex Adeptus Custodes, page 14:
The method by which such remarkable individuals are created has always been known only to those of the Imperial household, and is carried out by the most accomplished
chirurgeons and bio-alchemists of Terra within gilded laboratories locked away from the sight of Humanity’s masses. With the Adeptus Custodes fighting only for the Emperor himself, and beholden to the commands and scrutiny of no other, the secrets of their recruitment have never been revealed, for not even the High Lords of Terra have the right to demand them.
It is known that all Custodians begin their lives as the infant sons of the noble houses of Terra.
A Space Marine is created by the introduction of gene-seed to the body, as well as the implantation of supporting organs. Between them, these modifications reshape those who receive them into living weapons. By comparison, whatever mysterious bio-alchemy is used to trigger the transformation into a Custodian occurs on an entirely deeper level, taking root in the cells, perhaps even the soul, of an aspirant.
That much for the creation itself. According to the Codex, same page, for every worthy aspirant who succeeds, thousands are found wanting.
After the initial creation, their training begins:
The process of ascension goes beyond the purely physical and spiritual. Those who would join the brotherhood of the Adeptus Custodes are mentally indoctrinated; their psyches are rebuilt from the ground up, their mental architecture fortified as the Imperial Palace itself was fortified in the face of Horus’ treachery, until it becomes an impregnable fastness or else collapses under its own weight.
Each aspirant endures thousands of hours of such psycho-indoctrination and mnemic conditioning. Their education is mercilessly absolute, information beaten into the metal of their minds at a punishing rate that drives many mad. They must grasp not only the tenets of warfare in all its forms, and learn every method of assassination, counter-espionage, threat recognition and death dealing known to Mankind, but also expand their minds in far more esoteric directions. Diplomacy and statecraft, astrogation and interstellar geography, history, philosophy, theosophy, artistry and countless other subjects must all be mastered to a breathtakingly high degree.
But, no details are known about this, not even how long it takes to create a Custodes. Same Codex, page 15:
How long the process of creating a Custodian takes is unknown beyond the walls of the Imperial Palace.