The Syriac Orthodox Church is an autocephalous Oriental Orthodox church based in the Eastern Mediterranean, with members spread throughout the world. It employs the oldest surviving liturgy in Christianity, the Liturgy of St. James the Apostle, and uses Syriac as its official and liturgical language. The church is led by the Syriac Orthodox Patriarch of Antioch. The Syriac Orthodox Church traces its history to one of the first Christian communities, described in the Acts of the New Testament (Acts 11:26) and established by the Apostle St. Peter.

The Church belongs to the Oriental Orthodox family of churches, as such they recognize only the first three ecumenical councils.  There is much more to the story but the Syriac Orthodox Church became a distinct church body since the Council of Chalcedon in AD 451. Many in the Syrian Church were Nestorian so even the council of Ephesus was also problematic for some. The precise differences in theology that caused the split, "arose only because of differences in terminology and culture and in the various formulae adopted by different theological schools to express the same matter", according to a joint declaration by the head of the Syriac Orthodox church, Patriarch Mar Ignatius Zakka I Iwas, and Roman Catholic Pope John Paul II in 1984.

There is a Syriac Orthodox Archdiocese in North America who has a most informative site at http://www.syrianorthodoxchurch.org/. It does not comment on the issues of the canon as in the table below.  Wikipedia does not really address the issue of canonicity correctly either.  The existence of a book is a particular language does not necessarily mean that it is in common use by that church or even considered inspired.  From Catholic University we find:

The Syrian Orthodox Church believes that the Holy Bible, which comprises of the Old Testament and the New Testament, is the divine word of God. Its Fathers labored in translating the Holy Scriptures into Syriac since the very dawn of Christianity. These Syriac translations of the Bible are the oldest and most ancient in any language [as is acknoledged on the Peshitta page]. Further, the Syriac New Testament is quite unique for it presents the teachings of our Lord in an Aramaic dialect (Syriac) which is akin and would have been mutually comprehensible with the Palestinian dialect of Aramaic in which Christ taught. Since the translation of the Bible into Syriac started as early as the first century, the Syriac version preserves the very ancient renditions of the original texts. In fact, the Syriac Church Fathers produced a number of translations of the Bible and revisions of these translations from the original languages of the Bible. (http://sor.cua.edu/Bible/index.html 2/8/14)

Because of their geographical location and theology that is a bit different from that of even the Christian empires that ruled the area (Roman, Byzantine, Persian and Islamic), the church has often found itself persecuted.  It also had a front row seat for the rise of Islam and there are many who say that the Syrian and Nestorian Christians had great influence on what became Islam as Muhammad would have had contact with them.  

Another famous man is named Waraqa Ibn Naufal Ibn Assad (who died about the year 611). He was the bishop of Mekka that was full of Christians. He was the cousin of Khadidga, daughter of Khuailid, the wife of Muhammad, the prophet. Most of the Christians of Mecca, Yemen and Najran were members of the Syrian Orthodox Church. The majority of Qurash was Christian. (The Christians were called 'Nazarians' after Jesus.) As manifold as the different dogma of the Christians of the Arab peninsula might have been, they exercised a great influence upon their Arab Muslims there.

 

We do not want to forget that the main religious dogma of Christianity and Islam are close to each other, such as the belief in one God who made heaven and earth, the belief in the day of judgment, the day of the resurrection, eternal life, heaven and hell, etc. There are also historical-religious events of the Syrians, which are mentioned in the Quran, like the Legend of the Cave and The Martyrs of the Furrow. For the Syrians the Legend of the Cave was an event with which God proves that He, the creator, can bring back to life the dead on the day of the resurrection. It was handed down in the Syriac language in excellent style, verse and prose. It belongs to the Syrian tradition...  (http://www.syrianorthodoxchurch.org/library 2/8/14)

Although rare, there are references to Syriac in the translation notes of our English Bibles.  The Syriac tradition is an important witness to the continuity of the Church and the consistency of the gospel message.     

BooksProtestantRoman
Catholic
Syriac
Orthodox
Pentateuch
Genesis Yes Yes Yes
Exodus Yes Yes Yes
Leviticus Yes Yes Yes
Numbers Yes Yes Yes
Deuteronomy Yes Yes Yes
History
Joshua Yes Yes Yes
Judges Yes Yes Yes
Ruth Yes Yes Yes
1 and 2 Samuel Yes Yes Yes
1 and 2 Kings Yes Yes Yes
1 and 2 Chronicles Yes Yes Yes
Prayer of Manasseh Apocrypha No
(inc. in some mss.)
Yes (?)
Ezra
(1 Ezra)
Yes Yes
1 Esdras
Yes
Nehemiah
(2 Ezra)
Yes Yes
2 Esdras
Yes
1 Esdras
(3 Ezra)
I Esdras
(Apocrypha)
No
3 Esdras
(inc. in some mss.)

No (?)
(inc. in some mss.)

2 Esdras 3–14
(4 Ezra)
2 Esdras
(Apocrypha)
No
4 Esdras
(inc. in some mss.)

No (?)
(inc. in some mss.)

Esther  Yes Yes Yes
Additions to Esther Apocrypha Yes Yes
Tobit Apocrypha Yes Yes
Judith Apocrypha Yes Yes
1 Maccabees Apocrypha Yes Yes
2 Maccabees Apocrypha Yes Yes
3 Maccabees Apocrypha No Yes
4 Maccabees No No No (?)
(inc. in some mss.)
Josephus'sJewish War VI No No No
(inc. in some mss.)
Wisdom
Book of Job Yes Yes Yes
Psalms 1–150 Yes Yes Yes
Psalm 151 No No
(inc. in some mss.)
Yes
Psalms 152–155 No No Yes (?)
Psalms of Solomon No No No
(inc. in some mss.)
Proverbs Yes Yes Yes
Ecclesiastes Yes Yes Yes
Song of Songs Yes Yes Yes
Book of Wisdom Apocrypha Yes Yes
Sirach (1–51) Apocrypha Yes Yes
Prayer of Solomon
(Sirach 52)
No No (?)
(inc. in some mss.)
No
Major prophets
Isaiah Yes Yes Yes
Jeremiah Yes Yes Yes
Lamentations (1–5) Yes Yes Yes
Baruch Apocrypha Yes Yes
Letter of Jeremiah Apocrypha Yes
(chapter 6 of Baruch)
Yes
Syriac Apocalypse
of Baruch
(2 Baruch 1–77)
No No Yes (?)
Letter of Baruch
(2 Baruch 78–87)
No No Yes (?)
Ezekiel Yes Yes Yes
Daniel Yes Yes Yes
Additions to Daniel Apocrypha Yes Yes
Minor prophets
Hosea Yes Yes Yes
Joel Yes Yes Yes
Amos Yes Yes Yes
Obadiah Yes Yes Yes
Jonah Yes Yes Yes
Micah Yes Yes Yes
Nahum Yes Yes Yes
Habakkuk Yes Yes Yes
Zephaniah Yes Yes Yes
Haggai Yes Yes Yes
Zechariah Yes Yes Yes
Malachi Yes Yes Yes

http://en.wikipedia.org/wiki/Syriac_Orthodox_Church 2/8/14

http://en.wikipedia.org/wiki/Biblical_canon 2/8/14