The breadth of the patronymic

Theocritus, Idyll 15.120-122 ἀηδονιδεύς [ἀηδών, ἀηδονίς]:

οἱ δέ τε κῶροι ὑπερπωτῶνται Ἔρωτες,  
οἷοι ἀηδονιδῆες ἀεξομενᾶν ἐπὶ δένδρῳ
πωτῶνται πτερύγων πειρώμενοι ὄζον ἀπ’ ὄζω. 

And boyish Erotes flit overhead like young nightingales that flit upon the tree from spray to spray making trial of their fledgling wings [Gow, adapted].

cj. Valckenaer, ANU ἀηδονιῆες, KLWTr ἀηδονῆες.

Hesychius, 1503: <ἀηδονιδεύς·> ἀηδόνος νεοσσός. [καὶ τὸ τῆς γυναικὸς αἰδοῖον, παρὰ Ἀρχιλόχῳ (fr. 156)].
Note that this form is not in Archilochus. Archil.fr.263 West gives the lemma as ἀηδόνιον (as per Perizonius, codd. ἀηδόνων).

Buck-Petersen, p. 27 (final paragraph): 'Words in -ιδεύς: Only 28 of these are known... probably Debrunner... is right in identifying the -ιδ- with the patronymic suffix -ιδ-. In that case -ευς was humorously added because of its association with the dignified personal names like βασιλεύς 'king'. In favour of this is the total absence of -ιδεύς from serious poetry,... Rarely of human beings, as υἱϊδεύς (Isocr.) "son's son, grandson". Cf. also ἐρωτιδεύς (Anacreont.) "a young love".'.

Some others of interest from the Sibylline Oracles:

Βοοσπορίδης 'dweller on the Bosporos' (14.174: Steph.Byz. knows only these ethnic adjectives- Βοσπόριος/Βοσπορία, Βοσποριανός, Βοσπορηνός, and Βοσπορίτης as well as Βοσπορικός (τὸ κτητικόν the ktetic adjective).

Ἰταλίδης 'an Italian (native)' (4.104 and 12.85: but note that there was a king Italus, according to Vergil, Aeneid 7.178 and to Hyginus, Fabulae 127.3: see OLD s.v. Italus2);

Λατῐνίδης (5.1 and 12.1 Ἀλλ’ ἄγε μοι στονόεντα χρόνον κλύε Λατινιδάων (hexameter: note the quantity in comparison with Λατῖνος; also it seems that the alpha in Lat- must be long...).