Thanks to the efforts of various press agencies, there has been a story floating around the Internet this year about the "first Tamazight Quran". In reality, it's more like the last first Tamazight Quran. I'll try to describe the situation to date as best I can; if any readers know of relevant material I have omitted, please tell me!
You will find occasional reports online that the medieval Berghouata kingdom put together a Berber Qur'an translation; these are misunderstandings. If you look at what al-Bakri (the oldest source I can think of offhand for this) actually says about the Berghouata, he says their second king Salih ibn Tarif claimed to have received a revelation in Berber in 80 chapters which he called a Qur'an, but whose contents (some of which al-Bakri gives translated into Arabic) had nothing to do with the Qur'an. In fact, a later Berghouata king massacred thousands of Muslims in his kingdom for refusing to convert from Islam to the Berghouata religion. It would not surprise me at all to learn of a medieval Berber translation of the Qur'an; I know of such works for Turkish, Spanish, Persian, and Kanuri. However, discounting occasional ill-sourced reports of a no longer extant Almohad one, the earliest reference to such translation that I have come across is a fatwa by the Moroccan shaykh Al-Ḥasan bin Mas`ūd al-Yūsī in 1102 AH (1691 AD) judging translation of the Qur'ān into Tamazight to be permissible, mentioned in Jouhadi Hocine's translation's foreword; such a fatwa implies sporadic translation, but, as far as I am aware, no full written translation from the period has turned up.
Oral translations may be another matter. In Mali, there is reportedly a longstanding tradition of oral translation of the Qur'an into Tamasheq, the Berber language of the Tuareg; this was recorded in a series of 44 cassettes in 1989 by the Ahmed Baba Historical Documentation and Research Centre. Similar cases may well have existed elsewhere.
Serious published efforts at Qur'an translation seem to begin in the 1990s. The earliest partial translation to be printed seems to be Kamal Nait Zerrad's 1998 Lexique religieux berbère et néologie : un essai de traduction partielle du Coran. This work is primarily an effort to design a "purist" Berber religious vocabulary, one drawing on native lexical resources rather than Arabic borrowings, with a translation of a selection of suras added essentially as a proof of feasibility (the book's author, a well-known Berber linguist, does not in fact appear to be particularly strongly committed to Islam.) While the translation is basically into the author's native Kabyle, neologisms and words from other Berber varieties are so frequent as to make the translation rather difficult for native speakers of Kabyle to follow. This work uses the Latin orthography that has become more or less standard in Kabyle usage.
In 2003, with the Moroccan government's decision to raise the position of Tamazight and bring it into the school system, the first complete Berber Qur'an translation (strictly speaking, translation of the meanings of the Qur'an), Jouhadi Lhocine Baamrani's Tarjamat ma`ānī lqur'ān billuġati l'amāzīġiyyah: nūrun `alā nūr / tifawt f tifawt, many years in the making, finally appeared. This complete Moroccan translation (described years earlier, along with the political controversy surrounding it, by The Economist) has priorities more in accordance with one's expectations of such a work: the author's preface concerns itself primarily with reassuring the reader of the work's interpretative accuracy (the author uses the Warsh reading, and, in cases of difficulty, relies on examination of relevant hadith and well-known commentaries), and of the work's religious justification. However, conservative readers have expressed unease at his relative lack of religious training. The work is written in the Tashelhiyt of southern Morocco, a considerably less Arabic-influenced dialect than Kabyle; nonetheless, like Nait-Zerrad although not to the same extent, the author often chooses to use pure Berber vocabulary even when obscure in preference to Arabic loanwords, explicitly drawing an analogy to Fusha Arabic. "Some may say: I do not understand much of the Tamazight in which he has written, and I am Amazigh! I reply that not everyone who speaks Arabic, for example, understands the Qur'an which came down in faultless Arabic. Do not forget, dear reader, that a child spends much effort in gradually learning his native language, so why should you expect to know literary/pure (faṣīħ) Tamazight in a single go?" Apart from some Tifinagh on the cover, the author uses Arabic characters, regularly used by Tashelhiyt authors to write in their native language since the sixteenth century, although he substitutes a variant of Chafik's new orthography (writing all vowels as long instead of short, and using zay with three dots for the emphatic ẓ) which has grown in popularity. He has also published a translation of an-Nawawi's Forty Hadith, as well as some poetry.
Also in 2003, correlating to the Algerian government's gradual expansion of the role of Berber in efforts to conciliate opposition in Kabylie, a Kabyle translation of six hizbs, by Si Muḥend Muḥend Ṭayeb of the Ministry for Religious Affairs (with help from Said Bouziri, Djafar Oulefki, and Mohamed Tahar Ait Aldjet), was published by the King Fahd Complex for the Printing of the Holy Qur'an. This translation uses Arabic characters, but not in the systematic way of Jouhadi Lhocine's translation; rather than establishing a fixed phonemic orthography, it gives the impression of trying to fit Kabyle into Arabic characters in much the way that many people try to fit it into French ones, without any consideration for the phonemic rules of the language. For example, strictly phonetic assimilations across word boundaries, like n+r > rr, are written with shadda, and phonetically short a and ə are both written in the same way, with fatha. It was criticised by activists for its extensive use of Arabic vocabulary - although I rather suspect this makes it more readable to the average Kabyle speaker than the strict purism of other editions. A complete translation by the same people is to appear shortly; it is this which has been being carelessly reported as "the first Tamazight Qur'an".
However, when it does appear, it's not even going to be the first complete Kabyle translation. In late 2006, the poet and chemist Remḍan At Menṣur beat the Ministry to it; I saw copies of his complete translation in shop windows in Algiers and Paris, but have not yet got one. This work uses the Latin and Neo-Tifinagh orthographies on facing pages, and comes with an audio CD. The more extreme anti-Islamic wings of the Kabyle autonomy movement criticised the very fact of his translating this as promoting "Arabisation and Islamisation" (huh, who would have thought that translating the Qur'an might be construed as promoting Islam?) A more conservative reader, while praising the work, suggested that it would have been better off using Arabic script, and that the difficult task of translating with an eye to the correct interpretation required the efforts of a whole committee rather than a single man.
More translations are no doubt to be expected, and their quality - both interpretative and linguistic - will hopefully improve. But this cannot take place in isolation; the form Berber translations of the Qur'an end up taking will inevitably be heavily influenced by the form of the language that ends up being taught in the schools and used in other publications, and politics will continue to affect both whether and how the text is translated. It will be interesting to see how the situation develops.