Efratha regio Bethleem civitatis David, in qua natus est Christus. Est autem in tribu Iudae, licet plerique male aestiment in tribu Beniamin, iuxta viam, ubi sepulta est Rachel, quinto miliario ab Ierusalem in eo loco, qui a Septuaginta vocatur Hippodromus. Legimus Efratham et in Paralipomenon libro, sicut supra dictum est.
Eusebius, Onomasticon 82:10-14 (ca. 295 A.D.); Jerome 83:12-16 (ca. 390 A.D.)
Ephratha (Gen 35:16,19), the area of Bethlehem, the city of David, in which Christ was born. It belongs to the tribe of Judah, though many people wrongly ascribe it to the tribe of Benjamin. There they buried Rachel along the road, at the 'fourth' fifth milestone from Jerusalem, in the place which the Septuagint call the Hippodrome. 'Her tomb is shown to this very day. And the father of Bethlehem was called' Ephra-tha, as we read in the Chronicles (1 Chron 4:4), as we said above.
Gen 35:16-20 The death of Rachel
Then they journeyed from Bethel; and when they were still some distance from Ephrath, Rachel was in childbirth, and she had hard labor. 17 When she was in her hard labor, the midwife said to her, "Do not be afraid; for now you will have another son." 18 As her soul was departing (for she died), she named him Ben-oni; but his father called him Benjamin. 19 So Rachel died, and she was buried on the way to Ephrath (that is, Bethlehem), 20 and Jacob set up a pillar at her grave; it is the pillar of Rachel's tomb, which is there to this day.
Gen. 48:7 The burial place of Rachel
And as for me, when I came from Padan, Rachel died by me in the land of Canaan in the way, when yet there was but a little way to come unto Ephrath: and I buried her there in the way of Ephrath; the same is Bethlehem.
1Chr 4:4 "Ephratah, the father of Bethlehem"
And Penuel the father of Gedor and Ezer the father of Hushah. These are the sons of Hur, the firstborn of Ephratah, the father of Bethlehem.
MORE ANCIENT SOURCES
Hieronymus, Ep.108 (Peregrinatio Paulae) 10 (385 A.D.)
Going on towards Bethlehem, she paused where Rachel's Tomb stands on the right of the road, the birthplace of Benjamin - 'not Benoni', 'son of my sorrow' as his mother named him as she lay dying, but Benjamin 'son of my right hand', the prophetic name which his father gave him, inspired by the Holy Spirit...
Then, her joy mixed whith thears she began to say: "blessed Bethlehem, 'house of bread', birth place of the Bread that came down fron heaven! (Joh 6:33) Blessed Ephrata, 'Carpophorus' region most fertile, whose fertility is God! Of thee in old time Micah spoke this profecy, "And thou Bethlehem, house of Ephratah...