Following up on the preceding post, I've been looking at Greenberg's (1966) Nilo-Saharan comparisons - specifically, the 29 ones involving Songhay that have reflexes in Kwarandzyey, the Songhay language least likely to be involved in recent contact with Nilo-Saharan. Of these, 20 have comparanda in Saharan (Kanuri/Kanembu + Teda/Daza + Berti + Beria/Zaghawa), 17 in Eastern Sudanic (Nubian, Nilotic, Surmic, etc.), vs. a maximum of 13 for any other branch. (At least 7 also have plausible Mande comparisons.) Now, Saharan only consists of about 4 languages (9 by Ethnologue standards.) For Eastern Sudanic, excluding Kuliak, the Ethnologue counts 103 languages, and a huge amount of internal diversity. If Songhay were equally distant from the whole of Nilo-Saharan, you would expect far more cognates with Eastern Sudanic than with Saharan; the figures suggest that the link (whatever its nature) is primarily with Saharan, and only secondarily, if at all, with the rest of the languages he classified as Nilo-Saharan.
The grammatical comparisons that Greenberg offers are interesting but not compelling; there are only 10 of them (only 4 with Kwarandzyey reflexes), and they often incorporate misrepresentations (as Lacroix noted, for example, -ma forms verbal nouns, not relatives/adjectives, and 1sg ay < *agay, reducing the similarity to forms like Zaghawa ai.) Some of the lexical ones, however, are rather good; similarities such as Koyraboro Senni kokoši “scale (of fish)” = Manga Kanuri kàskàsí “scale (of fish)” cry out for explanation, and, though quite rare, look sufficiently numerous that chance seems unlikely. But whether they should be explained by contact or borrowing remains unclear. Either scenario would be historically interesting, since at present rather a large expanse of Tuareg and Hausa-speaking land separates Songhay from even Kanuri, and Saharan originated closer to modern-day Darfur than to Lake Chad.