Arabic Literature 

I have no information about this, apart from this short bibliography from Quasten, and material from George Khoury's articles, which I have excerpted below.

G. GRAF, Exegetische Schriften zum Neuen Testament in arabischer Sprache : BZ (1933) 22-40, 161-169. 
G. GRAF, Geschichte der christlichen arabischen Literatur. Rome 1944 and 1947. 5 vols. See also Arabic Christian Writers.
Philip HITTI, History of Syria. 

Link: http://www.ewtn.com/library/chistory/eveislam.htm - EASTERN CHRISTIANITY ON THE EVE OF ISLAM. Dr George Khoury.
Link: http://www.al-bushra.org/arbhrtg/arbxtn01.htm - Arabic Christian Literature. Dr George Khoury.
Link: http://www.al-bushra.org/mag08/earbxt.htm - Arab Christian Literature of the 8th-9th centuries, Dr George Khoury.

Catholicos Timothy I (728-823)

[Nestorians] Because of their number and importance in Mesopotamia, the Nestorians contributed more than any other Christian community to the Christian Arab literary heritage. Their activity comprises all the literary genres. 

In the first place stands out the Catholicos Timothy I (728-823). He was the protagonist and author of an interesting Muhawarah (debate) with the caliph al-Mahdi (775-785). 

Abu Nuh Ibn Al-Salt Al-Ambari (d. ?)

[Nestorian] Abu Nuh Ibn Al-Salt Al-Ambari was almost as important as Timothy I.  He was the translator of Greek works and author of Tafnid al Qur'an (Refutation of the Qur'an), Maqalat fi al-tawhid and Maqalat fi al-tatlit (Essaya on God's Unity and Trinity).

Al-Bitriq (8th century)

[Melkite] Al-Bitriq lived during the caliphate of al-Mansur (754-775), who commissioned him to translate numerous ancient medical works. He translated Galen's Simplicia under the name of al-adwiat al-mufrada; the De Prohibenda Sepultura and the De Cura Icteri of the pseudo-Galen under the name of Maqala fil-yaraqan. He also works attributed to Hippocrates: De Alimento, Kitabal-gida': De Septimanis, Kitab al-asabi, and he translated the Quadripartus of Ptolemeus, Kitab al-arabi'a. 

Theodore Ab Qurrah (750-820)

Theodore Abu Qurrah was a Christian Arab theologian who flourished in the early Islamic period. He seems to have been born in the city of Edessa, in the south of modern-day Turkey, and was for a time the Chalcedonian bishop of the nearby city of Harran. It is estimated that he died around the year 820 A.D.

Abu Qurrah was the author of over a dozen substantial treatises in Arabic. Also attributed to him are some forty smaller works in Greek. The subject matter of these treatises varies. Some defend Christian doctrine in the face of Muslim challenges. Others uphold Orthodoxy against a variety of Christian heretics, especially Monophysites and Nestorians. Yet others rearticulate traditional Christian teachings using the language and conceptual tools of Muslim theologians.

Early Christian Texts series.
Link: http://www.bautz.de/bbkl/t/theodoros_a_q.shtml (in German), with biblio.

Ammar al-Basri (c.800-850)

A Nestorian.  Ammar al-Basri (1st half of the 9th century) was a contemporary of the Melkite Abu Qurrah and the Jacobite Abu Ra'itah al-Takriti, and of the Nestorian Catholicos, Timothy I. Al-Basri wrote two apologetics: Book of the Demonstration and the Book of Questions and Answers.

Qusta Ibn Luqa (835-912)

Qusta Ibn Luqa was a Melkite from Baalbeck. He was an eminent translator and a theoretician of medicine. In addition, he was mathematician, physician, philosopher, apologist, and musician. Of him Ibn an-Nadim says: "Heis an excellent translator; he knew well Greek, Syriac, and Arabic; he translated texts and corrected many translations. Many are his medical writings." (see Ibn an-Nadim, Fihrist, ed. Fugel, p. 234.) Qusta was with Hunain Ibn Ishaq the author who best served Greek culture in the Arabcivilization.

Abu Raitah (Early 9th century)

[Jacobite] Habib Abu Ra'itah Al-Takriti (early 9th century) is a contemporary and a theological opponent of Theodore Abu Qurrah, Bishop of Harran. He is the author of four important theological treatise. 1. A letter on the Trinity addressed to a Muslim and in which he attempts to explain the mystery of the Trinity with the help of philosophical concepts of substance, hypostasis and essential attributes, such as life, knowledge, and wisdom, and with natural analogies, such as light, sun, man. He also quotes the Bible and the Qur'an. 2. A letter on the Incarnation in which he tries to explain the mystery of the Incarnation of our Lord Jesus Christ. 3. Demonstration of the truth of the Christian religion and of the doctrine of the Trinity.4. Proof of the truth of the Christian religion (however, this treatise may be inauthentic).

Hunayn ibn Ishaq (808-837).

Bibliophile.  Went searching for Greek literature and translated it.  Some discussion in L.D. REYNOLDS and N.G.WILSON, "Scribes and Scholars". 

A Nestorian.  Hunayn Ibn Ishaq (808-837)was a famous physician, philosopher, and translator of Greek works under several caliphs. He is the author of a Letter to Yahya ibn al-Munaggim.Yahya ibn al-Munaggim was a Muslim who invited Hunayn to convert to Islam.He also wrote a Letter on how to attain to the True Religion in which he shows that Christianity corresponds to the criteria of the true religion.His son Ishaq continued in his father's footsteps as translator and writer. From him we have Maqalah fi al-tawhid (Essay on Unity).

Sa'id ibn al-Bitriq, Patriarch of Alexandria from 933 to 940

[Melkite] There was also Sa'id ibn al-Bitriq, Patriarch of Alexandria from 933 to 940 and whose works put him on an equal footingwith Qusta ibn Luqa. In the field of medicine he wrote Kitab fi t-tibb(lost), in history, Kitab at-tarih al-magmu' ala t-tahqiq wa t-tasdiq, more commonlyknown under the name, Nazam al-gawahar. As apologist, he wrote in defense of Christianity, Kitab al-gadal baina l-muhalef wa n-nasrani.

Yahya Ibn 'Adi (d. 974)

One of the most prestigious of the Jacobite writers was Yahya ibn Adi (d.974): philosopher, polemist, and theolgian. His literary corpus comprises40 philosophical treatises, several treatises of apologetics, and his refutation of al-Kindi's refutation of the Christians. He was also a skilled translator of Plato and Aristotle.

Severus ibn al-Muqaffa (d. 987)

The Copts, who were of the Monophysite faith, adhered to their own language longer, and were almost one century later than the other Christian communities in expressing themselves in Arabic. Their contribution to the Arab Christian literature began with a great figure: Bishop of Asmunayn (Upper Egypt) Severus Ibn Al-Muqaffa (d. ca. 987). In theology, he wrote three important works: Book of the Exposition, Order of the Priesthood, and Precious Pearl. In apologetics he wrote: Book of the Councils and Brief Explanation ofthe Faith. He is best known though for his monumental History of the Patriarchs of Alexandria which was continued and completed in the 11th century by Michael, bishop of Tinnis and by Mawhub Ibn Mansur, deacon of Alexandria.

Elias of Nisibis (d. ca. 1049)

[Nestorian] Elias of Nisibis (Metropolitan of Nisibis (d. ca. 1049), known also as Elias bar Senaya, wrote as a dogmatic theologian two significant theological treatises:Letter on the Unity of the Creator and the Trinity of Persons and Letteron the Creation of the World. As apologist he wrote The Justification of Faith and Treatise on the Happiness of the Other World. He also bequeathed the report of Seven Sessions with the vizir al-Magribi. In the field of exegesis he wrote a Letter on the Difficulties of the Gospel.

Ibn at-Tayyib (1000-1050)

[Nestorian] Another important figure in the first half of the 11th century is Abdallah ibn al-Tayyib,physician, commentator of the Greek classics, philosopher and a prolificChristian writer. He wrote several treatises in systematic theology, one on moral theology and one on law. As biblical commentator he wrote more commentaries than any other Christian writer.

Further Jacobite Writers

There were also Musa al-Hagari (known as Moses Bar Kepha, died 903), and Al-Harith ibn Sinbat from Harran who were great biblical translators. But the most prestigious among them was Yahya ibn Adi (d. 974): philosopher, polemist, and theolgian. His literary corpus comprises 40 philosophical treatises, several treatises of apologetics, and his refutation of al-Kindi's refutation of the Christians. He was also a skilled translator of Plato and Aristotle. Issa ibn Zurah (Baghad, 1008), in addition to being an apologist and theologian, was also physician, philosopher, and scientist. Yahya ibn Garir from Takrit was physician, astronomer, philosopher, and theologian. His compendium in theology is call Kitab al-murshid.

Constructive feedback is welcomed to Roger Pearse.