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NIV Eph 2:2 in which you used to live when you followed the ways of this world and of the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient.

MGNT 2:2 ἐν αἷς ποτε περιεπατήσατε κατὰ τὸν αἰῶνα τοῦ κόσμου τούτου κατὰ τὸν ἄρχοντα τῆς ἐξουσίας τοῦ ἀέρος τοῦ πνεύματος τοῦ νῦν ἐνεργοῦντος ἐν τοῖς υἱοῖς τῆς ἀπειθείας

The #4 entry of BDAG has Aiwn in Ephesians 2:2 listed as an entity named Aeon!:

④ the Aeon as a person, the Aeon (Rtzst., Erlösungsmyst. 268 index
under Aion, Taufe 391 index; Epict. 2, 5, 13 οὐ γάρ εἰμι αἰών, ἀλλʼ
ἄνθρωπος=I am not a being that lasts forever, but a human being [and
therefore I know that whatever is must pass away]; Mesomedes 1,
17=Coll. Alex. p. 197, 17; Simplicius in Epict. p. 81, 15 οἱ αἰῶνες
beside the μήτηρ τῆς ζωῆς and the δημιουργός; En 9:4 κύριος τ. κυρίων
καὶ θεὸς τ. θεῶν κ. βασιλεὺς τ. αἰώνων; PGM 4, 520; 1169; 2198; 2314;
3168; 5, 468; AcPh 132 [Aa II/2, 63, 5]; Kephal. I p. 24, 6; 45, 7)
ὁ αἰ. τοῦ κόσμου τούτου Eph 2:2. The secret hidden from the Aeons Col 1:26; Eph 3:9 (Rtzst., Erlösungsmyst. 235f); IEph 19:2 (Rtzst. 86,
3); cp. 8:1 (Rtzst. 236, 2). Various other meanings have been
suggested for these passages.—CLackeit, Aion I, diss. Königsbg. 1916;
EBurton, ICC Gal 1921, 426–32; HJunker, Iran. Quellen d. hellenist.
Aionvorstellung: Vortr. d. Bibl. Warburg I 1923, 125ff; ENorden, D.
Geburt des Kindes 1924; MZepf, D. Gott Αιων in d. hellenist.
Theologie: ARW 25, 1927, 225–44; ANock, HTR 27, 1934, 78–99=Essays I,
’72, 377–96; RLöwe, Kosmos u. Aion ’35; EOwen, αἰών and αἰώνιος: JTS
37, ’36, 265–83; 390–404; EJenni, Das Wort ʿōlām im AT: ZAW 64, ’52,
197–248; 65, ’53, 1–35; KDeichgräber, RGG I3 193–95; HSasse, RAC I
193–204; MNilsson, Die Rel. in den gr. Zauberpapyri, K. humanist.
Vetenskapssamfundets Lund II ’47/48, 81f; GJennings, A Survey of αιων
and αιωνιος and their meaning in the NT, ’48; GStadtmüller, Aion:
Saeculum 2, ’51, 315–20 (lit.); EDegani, ΑΙΩΝ da Omero ad Aristotele
’61 (s. Classen, Gnomon 34, ’62, 366–70; D.’s reply in RivFil 91, ’63,
104–10); MTreu, Griech. Ewigkeitswörter, Glotta 43, ’65, 1–24; JBarr,
Biblical Words for Time2 ’69; OCullman, Christus u. die Zeit3 ’62.—B.
13. EDNT. DDD s.v. Aion. DELG. M-M. TW. Sv.

Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A
Greek-English lexicon of the New Testament and other early Christian
literature (3rd ed., p. 33). Chicago: University of Chicago Press.

I found more information HERE that shows that an Aion was "One of the embodiments of the divine attributes of the Eternal Being." This is fascinating as it gives a much clearer picture both of the role of the messiah and of the antichrist.

Here is a much more complete picture.

LSJ has this:

3. Αἰών, ὁ, personified, “Αἰὼν Χρόνου παῖς” E.Heracl.900 (lyr.), cf. Corp.Herm.11, etc.; as title of various divine beings, Dam.Pr.151, al.; esp.=Persian Zervan, Suid. s.v. Ἡραἰ̈σκος.

So I'm sold. But not everyone is. Most of the English translations I see either have "the course of" or "the ways of", neither of which are part of the semantic domain of AIWN. What is the argument for these translations and which is right?

It may very well be understood as one of the Aeons of Gnosticism. The apostle Paul commanded Timothy to remain at Ephesus and “charge certain people that they do not teach different teaching, nor give heed to myths and endless genealogies...”¹ These were not human myths and genealogies, but probably those of Gnosticism. Elsewhere to Timothy, the apostle Paul mentioned “antitheses of pseudonymnous gnosis”²Ã¢Â€Â”what appears to be a direct rebuke of Gnosticism.³

Tertullian wrote the following,⁴

And when he also mentions “endless genealogies” (1 Tim. 1:4), Valentinus is recognized, in whose writings that Aeon (I know not who) of a new and not single name generates from his own “Grace,” “Sense” and “Truth”; and in like manner, these produce from themselves “Word” and “Life,” and then these generate “Man” and “Church”—from which primary Ogdoad ten other Aeons then originate, and twelve remaining Aeons with wonderful names, in the mere fable of the thirty Aeons.

Sed et cum genealogias indeterminatas nominat (1 Tim. 1:4), Valentinus agnoscitur, apud quem Aeon ille nescio qui noui et non unius nominis generat e sua Charite Sensum et Veritatem; et hi aeque procreant ex se Sermonem et Vitam, dehinc et isti generant Hominem et Ecclesiam de qua prima ogdoade Aeonum exinde decem alii et duodecim reliqui Aeones miris nominibus oriuntur in meram fabulam triginta Aeonum.

Moreover, even if the apostle Paul gave mention to what he considered to be a false god, it was not because he believed it existed, but more likely that he “intends τὸν αἰῶνα τοῦ κόσμου τούτου to indicate the Devil in more polemic reference to the gnostic Aeon doctrine.”⁵ The remainder of Eph. 2:2 seems to lend credence to such an assertion.

Footnotes

¹ 1 Tim. 1:3–4
² 1 Tim. 6:20: «ἀντιθέσεις τῆς ψευδωνύμου γνώσεως»
³ Or a prototypical Gnostic religious system. The Gnostics claimed that they alone were privy to gnosis (γνῶσις).
⁴ Ch. 33, p. 46
⁵ Meyer, p. 90, Eph. 2:2: »soll τὸν αἰῶνα τοῦ κόσμου τούτου in polemischer Beziehung auf die gnostiche Aeonenlehre den Teufel bezeiehnen«

References

Meyer, Heinrich August Wilhelm. Kritisch exegetischer Kommentar über das Neue Testament, Achte Abtheilung, Kritisch exegetisches Handbuch über den Brief an die Epheser. 5th ed. Vol. 8. Göttingen: Vandenboeck and Ruprecht, 1878.

Quintus Septimius Florens Tertullianus. “Liber De Præscriptionibus.” Patrologiæ Cursus Completus: Series Prima. Ed. Migne, Jacques Paul. Vol. 2. Petit-Montrouge: Imprimerie Catholique, 1844.

αἰών could also be translated as age¹ in this instance (viz. "eon"). This is almost universally the meaning understood in ancient Greek (see, e.g., Liddell-Scott-Jones).

This, at least, is the sense understood by Theophylact (11th c. Byzantine Greek) in his commentary on the verse:

You did sin, then, and walked according to the age to which this world belongs, which means, thinking only about the passing things of this world and making poor use of the present age. It is not the world itself that is evil, but our misuse of it. This age, albeit corruptible and temporal, has been given to us by God as a guide to awaken us to love that which is incorruptible and immutable. But because we have devoted ourselves to the corruption of the age, we have made of the world an impediment rather than a guide.²

As you point out in the examples you provide, only a couple of translations use the word "age" here.

I haven't checked all translations, but of the 126 times that αἰών appears in the Greek text, the KJV translates the word as course only once - here in Ephesians 2:2. This might be a holdover from earlier English translations:

Tyndale (1536)

In the which in tyme passed ye walked/accordynge to the curse of this worlde & after the governer that ruleth in the ayer/the sprete that now worketh in the chyldrē of unbelefe*

Geneva Bible (1557)

Wherein, in time past ye walked, according to the course of this worlde, & after the prince that ruleth in the aire, even the spirit, that now worketh in the childrẽ of disobedience

According to the Oxford English Dictionary, one of the older meanings of "course" related to time:

III. fig. Of time, events, or action.
17.
a. The continuous process (of time), succession (of events); progress onward or through successive stages.
c1340 Cursor M. 267 (Laud 416) Cource of this world men shull yt calle.
1484 Caxton tr. G. de la Tour-Landry Bk. Knight of Tower (1971) lvii. 83 It is conuenyent that the tyme haue his cours.

1551 T. Wilson Rule of Reason sig. Xvj Throughout the whole course of this my rude and symple booke.

1569 R. Grafton Chron. II. 758 In the course of his life.

1576 A. Fleming tr. Erasmus in Panoplie Epist. 355 The yeare hath runne his course.

1647 C. Cotterell & W. Aylesbury tr. E. C. Davila Hist. Civill Warres France i. 3 The whole course of the Civill Warres.

1769 W. Robertson Hist. Charles V II. ii. 121 I return from it to the course of the history.

1882 J. H. Blunt Reformation Church of Eng. II. 23 The course of events which brought about this rapid fall.

1888 J. W. Burgon Lives Twelve Good Men I. i. 1 Four-and-thirty years have run their course since, etc.

b. The space of time over which any process extends; length (in time), duration. Obsolete.

1665 T. Herbert Some Years Trav. (new ed.) 234 The whole course of his [Noah's] life was 950 years.

1707 tr. P. Le Lorrain de Vallemont Curiosities in Husbandry & Gardening 65 The Course of its Life is sixteen Hours.

So one explanation for the prevalence of "course" is that it ties to an obsolete meaning of the word that was current at the time the King James Bible was published.³

^{1.See, e.g., A Greek-English Lexicon of the New Testament and Other Early Christian Literature (2nd ed.)
2.The Explanation of the Epistle of Saint Paul to the Ephesians (tr. from Greek; Chrysostom Press, 2013), p.30
3."Atonement" is another word in this category. A common meaning of the word today is "reparation for wrong or injury" (Concise Oxford English Dictionary, 11th ed.). According to the longer Oxford English Dictionary, the word did not take this meaning until late in the 17th century. Prior to and including the time that the KJV was published, "atonement" meant reconciliation, not reparation. Nonetheless many modern translations retain the word where it is used in older translations like the King James Bible, but ascribe the more modern meaning to it, essentially imputing a new definition to the underlying Greek or Hebrew that was not there in antiquity.}

Eph 2:1 & 2 is quintessentially Pauline in its brevity. Many wish that Paul had filled out his sentences a little more. Allow me to list the structure here with a literal translation:

v1: And you being dead in your trespasses and sins (v2) in which once you-walked

• according to [Gr kata] the age of this world


• according to [Gr kata] the ruler of the authority of the air

the spirit now working in the sons of disobedience.

The question should now be asked: are the two items (age of the world and ruler of the air) distinct or different names for the same thing. John uses a related phrase "ruler of this world" (John 12:31, 14:30, 16:11) to refer to Satan. Therefore, I believe they both refer to the same thing defined in two different ways by using some classic Hebrew parallelism.

So what does "age/aion" mean here? I think BDAG is correct in calling this a case of personification. Having said that, the person [ruler of the air] clearly dominates an era and its ways. Therefore, in keeping Paul's characteristic brevity, I would suggest that the intended meaning is both, and so I would translate this passage idiomatically as follows:

"And being dead in your trespasses and sins in which you once lived according to the ways of the ruler of the air who dominates this era, that is, the spirit now working in the sons of disobedience …"