For comparison's sake, here's a section from each.
The verse from "My Bonnie Lies over the Ocean":
My Bonnie lies over the oceanThe chorus of "Bluebirds over the Mountain":
My Bonnie lies over the sea
My Bonnie lies over the ocean
Oh, bring back my Bonnie to me
Bluebirds over the mountain
Seagulls over the sea
Bluebirds over the mountain
Bring my baby to me
The beginning of first section of "Daybreak over the Ocean" as they're rendered in the liner notes:
Daybreak over the oceanAll of these mention something either "over the ocean" or "over the sea" (or both) and end with the command to "Bring my baby/my Bonnie (back) to me." In both "Bluebirds over the Mountain" and "Daybreak over the Ocean," the structure of the first two lines is essentially the same: noun, preposition, article adjective, object of the preposition. "Daybreak over the Ocean" just adds an adverb ("still") for the second line. I feel it's also worth mentioning that Mike Love sings the lead vocals in both (and wrote "Daybreak over the Ocean").
Moonlight still on the sea
Will the waves gentle motion
Bring my babe my baby back to me
Both "My Bonnie Lies over the Ocean" and "Daybreak over the Ocean" also contain a whole section that's just variations on "Bring my baby/my Bonnie back to me." In "My Bonnie Lies over the Ocean," it's:
Bring back, bring backAnd in "Daybreak over the Ocean," it's:
Oh, bring back my Bonnie to me, to me
Bring back, bring back
Oh, bring back my Bonnie to me
Won't you bring back
Bring my baby back
Won't you bring back
Bring back my baby