Because the “books” of the Sibylline Oracles are from different periods it is necessary to briefly note the date and provenance for each. See this post for oracles 4-7, this post for oracles 8-14.
Sibylline Oracles Books 1-2. The first two books of the Sibylline Oracles form a unit. Lines 1-323 are a Jewish oracle which begin to recount the “ten generations” of human history. The first seven periods are covered in this section, but lines 324-400 are clearly Christian. After a brief transition in 2.1-5, 2.6-33 finished the “ten generations” theme. The eighth and ninth generations are missing; book two picks up with the tenth generation. SibOr 2.34-347 describes eschatological 
crisis and judgment. It is Jewish, but there are a number of lines which are Christian interpolations, especially in lines 45-264. The Jewish section of the book has been dated from 30 B.C. to A.D. 250 based on the dominance of Rome in the text. There is no reference to the fall of Jerusalem nor the Nero Myth (a frequent motif in later oracles.) Collins concludes that the Jewish sections date to pre-70, while the Christian interpolations date after 70, but no later than A.D. 150. There are numerous parallels between the second and eighth oracles, implying some literary dependence (which, assuming oracle eight used the second, implies the second was written first.) The Jewish section probably comes from Phrygia based on the reference in 1.196-198 to the ark landing in that country.
Sibylline Oracles Book 3. Lines 1-96 are probably a conclusion to another book. Lines 97-349, 489-829 are the “main book,” with an “Oracles against the nations” section inserted in 350-488. The main section expects God to intervene during the reign of the seventh king of Egypt (lines 193, 318, 608). The mostly likely candidates for the seventh king are Philometor (186-164, 163-145 B.C.), Neos Philopater (145-144 B.C.) and Physcon / Euergetes II (170-164, 164-163, 144-117 B.C.). Collins cites Valentin Nikiprowetzky, La Troisiéme Sibylle, (Paris: Mouton, 1970) as arguing the seventh king is Cleopatra VII (Athens, 85). As can be observed from the dates of these three kings, there are some co-regencies which complicate the chronology. Collins dates the book to 163-145 B.C. based on the prominence of Rome after 175 B.C. The book is definitely written after the battle of Magnesia, 190 B.C., (OTP 1:355).
This view has been challenged, however, by Rieuwerd Buitenwerf. He points out the numbering of Ptolemaic kings did not exist in antiquity. They were identified by “title.” The number seven is used three times in the context of the prediction of a seventh king, all figuratively according to Buitenwerf (cf. Erich Gruen, Heritage and Hellenism [Berkeley: University of California Press, 1998], 277). The writer of the oracle can only be said to believe that Roman rule will end when an Asian king conquers Egypt, signaling the appointed time for God to intervene in history. Therefore, the historical seventh king in the Ptolemaic dynasty does not matter for dating the book. Although he accepts the number seven may have been chosen as an ideal number, Collins disagrees that the seventh king has no bearing on the date. The prediction of God’s intervention when the seventh king reigns is meaningless if it is known there have been more than seven kings (Collins, Athens, 83-84, interacting with Erich Gruen).
Buitenwerf points out there is no hint of a Roman invasion of Palestine nor an end to the Ptolemy dynasty, therefore the book must be written some time before Actium, 31 B.C. He finds confirmation for this date in the paraphrase of Book 3 of the Sibylline Oracles by Alexander Polyhistor on the tower of Babel. His citation of lines 3.91-107 are preserved in Eusebius’ Chronica and Josephus’ Antiq. 1.118-119, although Josephus probably also used Polyhistor. Polyhistor began to write about 80 B.C. and died about 40 B.C.
Collins believes the main section of the book to be pro-Ptolemaic and therefore argues the book is the product of a diaspora Jew living in Egypt. This too has been challenged by Buitenwerf, calling the evidence for an Egyptian origin “extremely meager” (Buitenwerf, 131). He considers Collins’ evidence of a pro-Ptolemaic author as saying nothing of the sort and considers the topographical details as a reflection of “general education” (Buitenwerf, 132). He argues for an Asian origin for the book based on the frequent mention of Asian locations and (more importantly), the prediction that an Asian king will invade Egypt. Lines 367-380 predict this Asian king will usher in a time of bliss for Egypt, then again in lines 601-623 an Asian king invades and God intervenes in the world. The prophetess identifies herself as the Erythraean Sibyl, a very famous Asian prophetess. He concludes the author was a Jewish inhabitant of the Roman province of Asia. Collins agrees the “oracles against the nations” need to be dated a bit later, likely before the battle of Actium in 31 B.C., but the main section of the book, in Collins opinion, is earlier (Compendia rerum Iudaicarum 368-369). These are “gentile oracles” included to bring book three up to date and add to the sibylline flavor.
The first section is different from the rest of the book and is to be dated at least after Actium (line 46 seems to refer to the second Triumvirate.) Lines 75-92 refer to Cleopatra. Lines 63-92 are the most difficult to date, and ought to be considered separately from the rest of the introduction since they refer to the coming of Beliar. This looks like a Christian interpolation. The identity of Beliar may be Simon Magus as an anti-messiah, who was from Samaria (Herod’s renamed Samaria “Sebaste” in honor of Augustus in 25 B.C.)
A second and more likely possibility is the phrase describing Beliar ek Sebasttenon means “from the line of Augustus,” making Beliar Nero. This is in keeping with the Nero Myth and the common association of the return of Nero with an end-time villain. If the second option is accepted, then the date must be after A.D. 70 (when the Nero myth began to circulate), possibly later. The use of the Nero Myth in Revelation 13 is a bit controversial since most scholars date Revelation to the mid 90’s A.D. This would mean the Nero Myth was still common knowledge nearly 30 years after his death.
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