Oliver Cowdery initially wrote “the Eternal God” in the printer’s manuscript, then later (with somewhat heavier ink flow) corrected God to Father, probably when he was proofing against the original manuscript. Much earlier in 𝓟, Oliver made the same initial error, but this one he caught immediately and corrected inline:
The Book of Mormon text has quite a few examples of both “the Eternal God” (six times) and “the Eternal Father” (nine times), so either is theoretically possible here. However, when we consider the statistics for God versus Father when preceded by “covenant(s) of ”, there are only examples of Father (six in all, including this one in Moroni 10:31). In other words, there are no examples of “covenant(s) of God”; thus the corrected reading in Moroni 10:31 is what we expect based on other examples in the text.
Summary: Maintain in Moroni 10:31 the corrected reading in 𝓟, “the covenants of the Eternal Father”; this reading agrees with usage elsewhere in the text.