This is controversial subject you're inquiring into. You must know that there seems to exist a strong bias among Western scholars toward proving that original texts of New Testament were written in Greek. This bias seems to be rooted partially in tradition of Catholic and Orthodox Churches and is "inherited" by Protestants. Because of that everything NOT written in Greek is being seen as translation and sometimes strange theories are constructed about who and when translated New Testament. In reality, there exist quite a number of facts that may lead to think that original New Testament was written in Aramaic - and Greek and Latin manuscripts are but a poor quality copies. I would be VERY careful about anything you read about alleged translations made between Greek, Syriac and Aramaic. Also be VERY careful about what you read about Diatessaron, Old Syriac and Peshitta. I would advise to be VERY careful about dating of manuscripts and giving opinions thich one is "the best version". Such opinions can be VERY biased.
But about your question. One of the earliest complete manuscripts of Peshitta is Khabouris Codex (http://en.wikipedia.org/wiki/Khaboris_Codex) which is carbon-dated to 4th century but colophon states that it is a copy from older manuscript written in 164 AD. Apart of manuscripts there are found inscriptions on walls written in Estrangelo script which are dated to around 150 AD and are identical with what is found in Khabouris and other Peshitta codexes.
Khabouris is written in Aramaic. If you're interested in Syriac, then there is something you should know. There are at least two versions of pure syriac texts which are both younger by a few centuries from Khabouris. First version is tranlation from Aramaic Peshitta and second version is translation of Greek and Latin texts - probably even from Textus Receptus. This second version was created by European monks when they ventured from Europe to Asia to spread Christianity and they didn't know that Christianity was already there. They didn't understand ancient Aramaic but they've known Syriac and so they translated Greek and Latin into Syriac while ignoring already existing Peshitta. This is one of reasons of many misunderstandings about who was translating who.
Some others points that may be important in helping you determining what is what. Contrary to what Western scholars may say, internal evidence shows that Diatessaron was made from Peshitta not otherwise. Also Peshitta was not created by Rabulla, who created so-called Old Syriac from Greek sources. If you want to further read on these subject I would recommend looking for some Aramaic vs Greek Primacy disputes on the Internet. They're very lengthy, very detailed and show how greatly biased all the text criticism, archeology and manuscript dating is.
Something thay you might find interesting: http://en.wikipedia.org/wiki/List_of_the_Syriac_New_Testament_manuscripts