I finally got my hands on an article I had been looking for for a while about the "Kouriya" language of Gourara (around Timimoun, Algeria): Rachid Bouchemit, 1951. Le Kouriya du Gourara, Bulletin de Liaison Saharienne 5, p.46-47. While short, it's significantly more informative than the vague rumours to be found in other sources. "Kouriya", it turns out, was the general-purpose name given locally to any Black African language - "L'unité du terme cache la pluralité des idiomes: Haoussa, Bambra, Foullan, Mouchi, Songhai, Bornou, Boubou, Gouroungou, Minka, Sarnou, Nourma, Kanembou, Karkawi, etc...", in particular as spoken by ex-slaves in the region. Following the abolition of slavery, these languages, no longer reinforced by the arrival of new slaves, rapidly fell into disuse; the new generation learned Arabic and Taznatit instead. By 1951, the author could find only seven or eight speakers of a "Kouriya" in Timimoun, and only two of them spoke the same language, namely Bambara.
While the author leaves the etymology unexplained, I would add that the term "Kouriya", and the corresponding ethnonym kuri, probably derive from Songhay koyra "town, village", used to form the Songhays' own name for themselves, koyra-boro "townsman"; Songhay is, after all, the nearest major ethnic group in the Sahel to the Gourara region.