I believe Paul was saying that they were very religious. The idea of δεισιδαίμων is closer to "spirit-fearing", so for rationalists, this may be an insult, and for others it may be something like "god-fearing". I think it's less about two different senses of the word than two different attitudes toward those who fear and/or reverence the supernatural world.
Here is the BDAG[1] entry, which includes examples of laudatory usage. They recommend the translation in Acts of: I perceive that you are very devout people
δεισιδαίμων, ον, gen. ονος can, like δεισιδαιμονία, be used in a
denigrating sense ‘superstitious’ (cp. Maximus Tyr. 14, 6f in critique
of the δ. as a κόλαξ ‘flatterer’ of the gods μακάριος εὐσεβὴς φίλος
θεοῦ, δυστηχὴς δὲ ὁ δεισιδαίμων [s. H. app. and T.’s rdg.]; Philo,
Cher. 42; s. Field, Notes 125–27), but in the laudatory introduction
of Paul’s speech before the Areopagus Ac 17:22 it must mean devout,
religious (so X., Cyr. 3, 3, 58, Ages. 11, 8; Aristot., Pol. 5, 11 p.
1315a, 1; Kaibel 607, 3 πᾶσι φίλος θνητοῖς εἴς τʼ ἀθανάτους
δεισιδαίμων) comp. for superl. (as Diog. L. 2, 132):
δεισιδαιμονεστέρους ὑμᾶς θεωρῶ I perceive that you are very devout
people Ac 17:22 (the Athenians as the εὐσεβέστατοι τ. Ἑλλήνων: Jos.,
C. Ap. 2, 130. Cp. Paus. Attic. 24, 3 Ἀθηναίοις περισσότερόν τι ἢ τοῖς
ἄλλοις ἐς τὰ θεῖά ἐστι σπουδῆς).—DELG s.v. δαίμων. TW. Spicq.
I also recommend the TDNT entry[11]:
General expression for “piety,” the more precise sense varying
according to the two constituents δείδω == “to fear” (ἔδεισα) and
δαίμων. Thus δεισιδαιμονία may on the one side denote a “pious
attitude towards the gods,” i.e., “religion,” and on the other
“excessive fear of them.” In general, however, it is not used in the
non-Christian world for “superstition,” i.e., fear of evil spirits,
since the Greeks hardly see the radical distinction between gods and
spirits, and could only have a poor sense of any such distinction. Yet
there is sometimes present a certain fear of spirits.
Some examples of usages:
Negative sense
Philo: On the Cherubim, 42:
(42) But that we may describe the conception and the parturition of
virtues, let the superstitious either stop their ears[5]
ἵνα δὲ τὴν ἀρετῶν κύησιν καὶ ὠδῖνα εἴπωμεν, ἀκοὰς ἐπιφραξάτωσαν οἱ
δεισιδαίμονες τὰς ἑαυτῶν ἢ μεταστήτωσαν [6]
Philo, The Worse is Want to Attack the Better, 18:
For as it is of no use to study music in an unmusical manner, nor
grammar without any attention to its true principles, nor, in short,
any art whatever in a manner either devoid of art or proceeding on
false rules of art, but each art must be cultivated on a strict
obedience to its rules; so also it is of no avail to apply one’s self
to the study of wisdom in a crafty spirit, or to the study of
temperance in a nigardly and illiberal frame of mind, nor to courage
rashly, nor to piety superstitiously, nor, in fact, to any other
science which is in accordance with virtue in an unscientific manner.[5]
ὥσπερ γὰρ οὔτε μουσικὴν ἀμούσως οὔτε γραμματικὴν ἀγραμμάτως οὐδὲ
συνόλως φράσαι τέχνην ἀτέχνως ἢ κακοτέχνως ἀλλὰ τεχνικῶς ἑκάστην
ἐπιτηδεύειν προσῆκεν, οὕτως οὐδὲ φρόνησιν πανούργως οὐδὲ σωφροσύνην
φειδωλῶς καὶ ἀνελευθέρως οὐδὲ θρασέως ἀνδρείαν οὐδὲ δεισιδαιμόνως
εὐσέβειαν οὐδʼ ἄλλην τινὰ τῶν κατʼ ἀρετὴν ἐπιστήμην ἀνεπιστημόνως
ἀνοδία γὰρ ὁμολογουμένως ταῦτα πάντα. [12]
Clement of Alexandria. Against the Hellenes, X:
Fishes do not fear demons, birds do not worship idols [13]
οὐ δεισιδαιμονοῦσιν ἰχθύες, οὐκ εἰδωλολατρεῖ τὰ ὄρνεα [14]
Positive sense
Xenophon, Agesilaus 11.8:
He was ever god-fearing, believing that they who are living life well
are not yet happy, but only they who have died gloriously are blessed.[2]
Ἀεὶ δὲ δεισιδαίμων ἦν, νομίζων τοὺς μὲν καλῶς ζῶντας οὔπω εὐδαίμονας,
τοὺς δὲ εὐκλεῶς τετελευτηκότας ἤδη μακαρίους. [3]
Xenophon Cyropaedia, 3.3.58
And they all devoutly joined with a loud voice in the singing, for in
the performance of such service the God-fearing have less fear of
men.[7]
οἱ δὲ θεοσεβῶς πάντες συνεπήχησαν μεγάλῃ τῇ φωνῇ· ἐν τῷ τοιούτῳ γὰρ δὴ
οἱ δεισιδαίμονες ἧττον τοὺς ἀνθρώπους φοβοῦνται. [8]
Aristotle, Politics, 1315a.1
if they think that their ruler has religious scruples and pays regard
to the gods, and also they plot against him less, thinking that he has
even the gods as allies)[9]
ἐὰν δεισιδαίμονα νομίζωσιν εἶναι τὸν ἄρχοντα καὶ φροντίζειν τῶν θεῶν,
καὶ ἐπιβουλεύουσιν ἧττον ὡς συμμάχους ἔχοντι καὶ τοὺς θεούς)[10]
[1] William Arndt et al., A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), 216.
[2] Xenophon, Scripta Minora, trans. E. C. Marchant, The Loeb Classical Library (London; Cambridge, MA: William Heinemann Ltd; Harvard University Press, 1925), 131.
[3] Xenophon, “Scripta Minora: Greek Text,” The Loeb Classical Library (London; Cambridge, MA: William Heinemann Ltd; Harvard University Press, 1925), 130.
[4] Flavius Josephus and William Whiston, The Works of Josephus: Complete and Unabridged (Peabody: Hendrickson, 1987), 801.
[5] Charles Duke Yonge with Philo of Alexandria, The Works of Philo: Complete and Unabridged (Peabody, MA: Hendrickson, 1995), 84.
[6] Peder Borgen, Kåre Fuglseth, and Roald Skarsten, “The Works of Philo: Greek Text with Morphology” (Bellingham, WA: Logos Bible Software, 2005).
[7] Xenophon, Xenophon in Seven Volumes, 5 and 6, trans. Walter Miller (Medford, MA: Harvard University Press, Cambridge, MA; William Heinemann, Ltd., London., 1914).
[8] Xenophon, “Cyropaedia: Greek Text,” ed. T. E. Page and W. H. D. Rouse, The Loeb Classical Library (London; New York: William Heinemann; The Macmillan Co., 1914), 298.
[9]Aristotle, Aristotle in 23 Volumes, Translated by H. Rackham., vol. 21 (Medford, MA: Cambridge, MA, Harvard University Press; London, William Heinemann Ltd., 1944).
[10]Aristotle, “Ed. W. D. Ross, Aristotle’s Politica” (Medford, MA: Oxford, Clarendon Press, 1957).
[11] Werner Foerster, “Δαίμων, Δαιμόνιον, Δαιμονίζομαι, Δαιμονιώδης, Δεισιδαίμων, Δεισιδαιμονία,” ed. Gerhard Kittel, Geoffrey W. Bromiley, and Gerhard Friedrich, Theological Dictionary of the New Testament (Grand Rapids, MI: Eerdmans, 1964–), 20.
[12] Peder Borgen, Kåre Fuglseth, and Roald Skarsten, “The Works of Philo: Greek Text with Morphology” (Bellingham, WA: Logos Bible Software, 2005).
[13] T. E. Page et al., eds., Clement of Alexandria, trans. G. W. Butterworth, The Loeb Classical Library (Cambridge, MA; London: Harvard University Press; William Heinemann, 1960), 231.
[14] T. E. Page et al., eds., Clement of Alexandria: Greek Text, trans. G. W. Butterworth, The Loeb Classical Library (Cambridge, MA; London: Harvard University Press; William Heinemann, 1960), 230.
