In the end it gets down to
the simple matter of if
Ents are
animals or
plants. If animals they will have sex as animals do, if plants they'll do it like plants.
Since they move around and don't appear to photosynthesize for a living and were apparently created to defend the forests from the other children of Illuvatar, my take is that they are animals and that they therefore have babies like animals.
That gives them considerable leeway: they could lay eggs/seeds like reptiles or have young that go through a complicated life cycle like insects; perhaps spending their first twenty years or so as
trees and then coming to life and being Ents, for example.
Whatever the case they are unique even among the free
peoples, among whom enthusiasm for reproduction is conspicuous by its absence, in being so uninterested in the perpetuation of their species that the sexes separated permanently.
Such a species is surely doomed. Not only did they fail in their appointed task of defending the forests, but they failed even to defend themselves from the slow decay of time by keeping their numbers up.