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 1-3, this post for oracles 4-7.
Sibylline Oracles Book 8. The eighth oracle is a composite of two works. The first half of the book (lines 1-216) has been described as entirely Christian (Geffcken) or Jewish (Rzach), although it is probably best to see the section as a Christian redaction of a primarily Jewish work, probably under the influence of the book of Revelation (OTP 1:415-416). The first half can be dated during 
the reign of Marcus Aurelius (d. 180) since line 148 appears to predict Nero’s return in the reign of Aurelius (year 948 of Rome.) The second half of the book (217-500) appears Christian, possibly relying on the Christian section of Sibylline Oracles 2 (OTP 1:416). Lactantius used the second half of the book extensively, but there is nothing in the section to help fix a date prior to A.D. 300.
Sibylline Oracles Book 11-12. The last four of the sibylline books form a unit since they are a continuous outline of history. The later books appear to have been appended to bring the outline of history “up-to-date.” Book eleven may end at the death of Cleopatra, although this is a challenged point (Compendia rerum Iudaicarum, 375-376, OTP 1:431-432). A date of the “turn of the era” is the best, but there is no doubt in Collins mind the book comes from Egypt because of the prominence of Cleopatra. If books 11 and 12 form a continuous unit, then the date needs to be pushed back to the third century since the book ends with Alexander Severeus (A.D. 218-235).
Sibylline Oracles Book 13. The beginning of this book appears lost since the history resumes with Gordianus (A.D. 240-244). Since it ends without mentioned the death of Odenath of Palmyra, the book is to be dated “with confidence” to A.D. 265 (Odenath took the title “king” when Valerian I was captured, Collins OTP 1:458, note d2). Like the previous two books, it was likely written from Alexandria, Egypt. The book has very little theological content, making a decision on Jewish / Christian authorship impossible.
Sibylline Oracles Book 14. This last oracle is described by Collins as a reductio ad absurdum for the whole sibylline genre. He cites Geffcken’s assessment: the writer was “a Phantast . . . an ignoramus who knew nothing except names of people, countries and cities, and arbitrarily mixes them . . .” (OTP 459; Note 7 references Boussett in Real-Encyclopedia who assumes the work is Christian without arguing the case).
The book probably comes from the seventh century, written by an Alexandrian Jew with no hint of Christian redactions. W. Scott thought the book referred to the Arab conquest of Egypt, placing the date in the seventh century (W. Scott, “The Last Sibylline Oracle” Classical Quarterly 9 (1915), 144-166; 207-228, 10 (1916) 7-16).
Sibylline Fragments. Collins lists eight fragments of oracles which are found in Theophilus Ad Autolcycum 2.36 (fragment 1, 3) and 2.3 (fragment 2). Lactantius has fragments 4-7 and fragment 8 is referenced in Constantine’s “Speech to the Saints” The authenticity of the Theophilus fragments has been doubted. Geffcken thought Theophilus forged them himself (OTP 1:467).
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