There is no rite of Ordination for a Transitional Deacon with a separate rite for a Permanent Deacon.
Not only that, there is also no “permanent” diaconate and “transitional” diaconate. Those are short-hand, inaccurate, terms. There is but
one diaconate. Some men may serve as deacons for a short time if they are destined for the presbyterate, and others serve as deacons without plans for the presbyterate.
We have a TON of deacons here in my archdiocese (more than we have priests), and our current archbishop did move the ordination date up for deacons a few years ago (there were no seminarians being ordained deacons that year) to a few weeks before presbyteral ordination.
We have also had ordinations of both seminarians and diaconal candidates in the same Mass, as well.
Some of the EC churches do not have permanent deacons. I was wondering if an EC could become a permanent deacon in the Latin Church?
I am not sure this is technically accurate - all Eastern Churches have deacons, even if they just serve for a short time before priestly ordination. Many Eastern Churches don’t want men to remain as deacons very long (not because they do not value the diaconate) because they are desperate for priests.
In any event, if there were an Eastern Catholic man who was interested in the diaconate and his Eparchy didn’t want a deacon – arrangements could be made to form and ordain him for a different Eastern Church, or, he could [theoretically] change rites and study/become a western deacon.
There are some Eastern Churches where the priests serve in a way similar to Western deacons, by the way. They have another job, often working during the week at
that job, and serving primarily a little Temple on the weekend, for example.