As you say you are writing a paper, I'll assume you have access to JSTOR. Take a look at this paper:
David M. Jacobson
Bulletin of the American Schools of Oriental Research No. 313 (Feb., 1999), pp. 65-74 Published by: The American Schools of Oriental Research
Here's the abstract
"This article critically reexamines the origin of the name Palestine. The earliest occurrence of this name in a Greek text is in the mid-fifth century B. C., Histories of Herodotus, where it is applied to the area of the Levant between Phoenicia and Egypt. Josephus, the Jewish historian of the first century A. D., explicitly links this name to the land of the Philistines and modern consensus agrees with him. Yet, some 300 years earlier, the translators of the Greek Septuagint version of the Pentateuch chose Philistieim rather than Palaistinoi to describe the Philistines. In the earliest Classical literature references to Palestine generally applied to the Land of Israel in the wider sense. A reappraisal of this question has given rise to the proposition that the name Palestine, in its Greek form Palaistinē, was both a transliteration of a word used to describe the land of the Philistines and, at the same time, a literal translation of the name Israel."
We know Syria Palestina was a province after the time of Hadrian, and have coins with that name from the time of Aurelius. We also know that Hadrian was very vindictive to the Jews (there's a bas-relief somewhere of him killing one personally) so I think most historians draw the obvious conclusion. However if nothing but the original sources will do, you might also try Eusebius bk 6 there might be something there.