The Romans did, in fact there were several cosmogonies (which is what the Hesiod's Theogony partly is), with theogonic elements. The most notable example of this is Ovid's Metamorphoses, specifically the earliest sections of it. In the Greco-Roman world there were others as well. Though only fragments survive, this existed in Philo of Byblos' Phoenician History additionally, which is a Hellenized Canaanite account of the narrative.

A very closely related text and theogony as well is the Hurrian/Hittite tale of Kumarbi or the Song of Kumarbi. This is very closely related to Hesiod's Theogony as well.

Unlike Hesiod's tale, the Roman equivalent in Ovid is not made with the explicit purpose of depicting the origins and genealogy of the gods themselves, but ultimately Ovid makes use of numerous themes and narratives, not all of which are truly connected entirely, in a loose mythical "history" up to the time at when Julius Caesar became worshiped as a god by the Romans. Hesiod's Theogony on the other hand is based around the myth of succession, which is actually a series of succession myths ending with Zeus as the final ruler of the universe when he defeats his father, who in turn had defeated Uranus before.

I would suggest reading Stephen Scully's Hesiod's Theogony: From Near East Creation to Paradise Lost (Oxford UP, 2015) on this topic.