Wanting examples of expressing a year when something took place, I found Josepus having a little relevant material in his Ἰουδαϊκὴ ἀρχαιολογία. Writing in the 1st century, he used the Olympiad reckoning, which seems to have been introduced by historians in the 200’s BCE. Examples of the older Athenian eponymous reckoning custom have to be searched from some other author.
1. τῷ τρίτῳ ἔτει τῆς ἑϐδόμης καὶ ἑϐδομηκοστῆς πρὸς ταῖς ἑκατὸν ὀλυμπιάδος, ὑπατεύοντος Ῥωμαίων Κυίντου Ὁρτησίου καὶ Κυίντου Μετέλλου. (14,4)
‘In the third year of 177th Olympiad, when Q. Hortensius and Q. Metellus were consuls, — —’
Notes. datiuus temporis for ‘in 3rd year’. ‘Of the 177th Olympiad’ is expressed by τῆς — — ὀλυμπιάδος, numbers from small to large. One would, however, expect “καὶ ἑκατοστῆς ὀ.”, would one not? J. uses instead πρὸς ταῖς ἑκατὸν, i.e. cardinal. Is this a commun custom? How would it be analysed? What is the omitted headword of ταῖς? Maybe of lesser surprise is the gen. sg. ὑπατεύοντος in the genetiuus absolutus; it refers to two persons, and besides Ῥωμαίων is in gen. pl.
2. περὶ τρίτον μῆνα τῇ τῆς νηστείας ἡμέρᾳ κατὰ ἐνάτην καὶ ἑϐδομηκοστὴν καὶ ἑκατοστὴν ὀλυμπιάδα ὑπατευόντων Γαΐου Ἀντωνίου καὶ Μάρκου Τυλλίου Κικέρωνος. (14,66)
‘In the third month, on the day of fast, in the 179th Olympiad, when C. Antonius and M. Tullius Cicero were consuls, — —’
Notes. περὶ + acc. for ‘in the 3rd month’; dat. temp. for ‘on the day of fast’. κατὰ + acc. (κατὰ — — ὀλυμπιάδα) for the year, numbers from small to large. Now we have gen. pl. ὑπατευόντων in gen. abs.
3. ἑστιᾷ δὲ τὴν πρώτην ἡμέραν τῆς βασιλείας Ἀντώνιος. καὶ ὁ μὲν οὕτως τὴν βασιλείαν παραλαμϐάνει τυχὼν αὐτῆς ἐπὶ τῆς ἑκαστῆς καὶ ὀγδοηκοστῆς καὶ τετάρτης ὀλυμπιάδος ὑπατεύοντος Γναίου Δομετίου Καλϐίνου τὸ δεύτερον καὶ Γαΐου Ἀσινίου Πωλίωνος. (14,389)
‘Antonius feasts the first day of rule (or: in the first day of rule?). In this way he got the kingdom, having chanced upon it in the 184th Olympiad, when Cn. Domitius Caluinus was for the second time a consul, and C. Asinius Pollio his first time.’
Notes. Is ἑστιᾷ lively praesens historicum usage? Would τὴν πρώτην ἡμέραν be best considered its object, or rather accusatiuus temporis (‘for the length of the first day’)? The time when is here with ἐπὶ + gen., now from large to small.
4. τῆς γὰρ ἐπ’ Ἀκτίῳ μάχης προσδοκωμένης, ἣν ἐπὶ τῆς ἑϐδόμης καὶ ὀγδοηκοστῆς πρὸς ταῖς ἑκατὸν ὀλυμπιάδος συνέϐη γενέσθαι, Καῖσαρ μὲν Ἀντωνίῳ περὶ τῶν ὅλων ἔμελλεν ἀγωνιεῖσθαι πραγμάτων. (15,109)
‘The Battle of Actium being expected. It came to pass in the 187th Olympiad, when Augustus was to fight Antonius about all the things.’
Notes. Begins with gen. abs., the time when in the relative clause is marked with ἐπὶ + gen., and again we have the πρὸς ταῖς ἑκατὸν embedded before ὀλυμπιάδος.
5. Συνέϐη δὲ μετὰ ἔτη δύο τῷ ἑκατοστῷ καὶ τεσσαρακοστῷ καὶ πέμπτῳ ἔτει μηνὸς πέμπτη καὶ εἰκάδι, ὃς καλεῖται κατὰ μὲν ἡμᾶς Ἐξελέους, κατὰ δὲ Μακεδόνας Ἀπελλαῖος, ὀλυμπιάδι ἑκατοστῇ καὶ πεντηκοστῇ καὶ τρίτῃ. (12,248)
‘It happened after two years, in the 145th year, on the 25th day of month, which we call Ἐξελέους (?), Macedonians Apellaios, in the 153rd Olympiad.’
Notes. Where does 145th year refer to? Why is it needed in the 1st place? Ἐξελέους is apparently some Hebrew month; it’s not in the LS. “When” is marked with a regular dat. temp.
6. Ἀντίοχος δὲ χαλεπῶς ἔχων ἐφ’ οἷς ὑπὸ Σίμωνος ἔπαθεν εἰς τὴν Ἰουδαίαν ἐνέϐαλεν τετάρτῳ μὲν ἔτει τῆς βασιλείας αὐτοῦ, πρώτῳ δὲ τῆς Ὑρκανοῦ ἀρχῆς, ὀλυπιάδι ἑκατοστῇ καὶ ἑξηκοστῇ καὶ δευτέρᾳ.
‘Antiochus was angry for what Simon had had to go through. He left for Judaea in his fourth year of reign. That was the first year when Hyrcanus ruled, and occurred in the 162nd Olympiad.’
Notes. This has three datiui temporis.