When did Arabic enter into usage as a liturgical language among Christian Churches?
Arabic became a liturgical language in the 12th century.
The official language of Egypt is Arabic, and most Egyptians speak one of several vernacular dialects of that language. As is the case in other Arab countries, the spoken vernacular differs greatly from the literary language. Modern literary Arabic (often called Modern Standard Arabic or al-fuṣḥā, “clear” Arabic), which developed out of Classical, or medieval, Arabic, is learned only in school and is the lingua franca of educated persons throughout the Arab world. The grammar and syntax of the literary form of the language have remained substantially unchanged since the 7th century, but in other ways it has transformed in recent centuries. The modern forms of style, word sequence, and phraseology are simpler and more flexible than in Classical Arabic and are often directly derivative of English or French.
At the time of the Islamic conquest, the Coptic language, a latter incarnation of the ancient Egyptian language, was the medium of both religious and everyday life for the mass of the population. By the 12th century, however, Arabic had come into common use even among Christian Copts, whose former tongue continued only as a liturgical language for the Coptic Orthodox Church.
Copts are far and away the largest Christian denomination in the country. In language, dress, and way of life they are indistinguishable from Muslim Egyptians; their church ritual and traditions, however, date from before the Arab conquest in the 7th century. Ever since it broke with the Eastern Church in the 5th century, the Coptic Orthodox Church has maintained its autonomy, and its beliefs and ritual have remained basically unchanged. The Copts have traditionally been associated with certain handicrafts and trades and, above all, with accountancy, banking, commerce, and the civil service; there are, however, rural communities that are wholly Coptic, as well as mixed Coptic-Muslim villages. The Copts are most numerous in the middle Nile valley governorates of Asyūṭ, Al-Minyā, and Qinā. About one-fourth of the total Coptic population lives in Cairo. - Languages (ENCYCLOPÆDIA BRITANNICA)
Samn's response to this question leads one to believe that Arabic as a liturgical language stated in the 8th century. However that is easily refuted for a later date as the following article clearly demonstrates: The identity and witness of Arab pre-Islamic Arab Christianity: The Arabic language and the Bible.
Because of these two problems, no Arab Eusebius and no clear definition of arabness, we have difficulty in uncovering the story of the Arabs, and especially the Arab Christians, from their own perspective in antiquity. It is not until the 6th century that we find Arabs using the Arabic script to leave any form of cultural self-identification. The poetry of pre-Islamic Arabs is the first genre of indigenous literature where the history of the Arabs can be gleaned from their own perspective; and even so, most of the collections of these 6th century poets are the result of 8th century editors (Hoyland 2001:212-220).The general murkiness of the historical sources on the Arabs is difficult enough, let alone our inquiry into what Arab Christianity actually signifies. Nevertheless, if we look closely we find the evidence.
The middle of the 7th century created unique problems for the development and use of a public Arab Christian text. As Kenneth Cragg famously wrote, Arab Christians are linguistically defined by a language that is 'bound over to the Qur'an' (Cragg 1991:65). To put it another way, as the Qur'an has served as the standard of the Arabic language since its own binding, Arab Christians have had to engage in their own self-discovery of what it means to be Arab apart from the arabnessof the Qur'an. For some Arab Christians this has meant upholding the Islamic tradition as one important Arab cultural legacy. For others it has meant jettisoning the Arab veneer and looking for the pre-Islamic identities of the Phoenicians or Pharaohs. At other points in history, Arab Christians have tried to define their Arabness as an imperial imposition that has been forced upon their previous own cultural identities.
Thus it was only after the appearance of the Qur'an that Christians truely started writing in Arabic for apologetics and scriptural purposes. Its' use as a liturgical language was much later.