English translations don't necessarily render this as "On a Sabbath" or "One Sabbath" because the meaning of the term is uncertain, but because there are textual difficulties here as well. While the term appears in a number of manuscripts (A, C, D, L, Δ, Θ, Ψ, Byz, many Itala), it is also missing from many as well (P4, P75, א, B, L, W, family 1, many Itala, Syriac). That said, part of the reason some textual scholars believe it to be the error of a later copyist is that it is a unique term, appearing only here in the extant literature.
For instance, Bruce Metzger proposes the following scenario:
The word δευτεροπρῶτος occurs nowhere else, and appears to be a vox nulla that arose accidentally through a transcriptional blunder. Perhaps some copyist introduced πρώτῳ as a correlative to ἐν ἑτέρῳ σαββάτῳ in ver. 6, and a second copyist, in view of 4:31, wrote δευτέρῳ, deleting πρώτῳ by using dots over the letters—which was the customary way of cancelling a word. A subsequent transcriber, not noticing the dots, mistakenly combined the two words into one, which he introduced into the text.
Metzger, B. M., United Bible Societies. (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies’ Greek New Testament (4th rev. ed.) (p. 116). London: United Bible Societies.
As you can see, Metzger's proposal includes the possibility that δευτεροπρῶτος was not a word at all, but the result of a copyist's mistake. BDAG similarly suggests, "it may owe its origin solely to a scribal error." And it's not just modern translators who have struggled with it; Jerome wrote about it (Letter LII, 2):
My teacher, Gregory of Nazianzus, when I once asked him to explain Luke’s phrase σάββατον δευτερόπρωτον, that is "the second-first Sabbath," playfully evaded my request saying: "I will tell you about it in church, and there, when all the people applaud me, you will be forced against your will to know what you do not know at all. For, if you alone remain silent, every one will put you down for a fool."
While there is significant agreement that the meaning of the word is difficult to ascertain, there are a number of proposals. BDAG, for instance, suggests that "it might correspond (but s. M-M.) to δευτερέσχατος (=next to the last) and mean first but one." It's hard to see why Luke wouldn't just opt for δευτέρῳ, though.
Darrell Bock (BECNT) offers four more (with comments), citing Plummer (ICC) and Fitzmyer (AB):
- It is the first Sabbath in the second year of the seven-year cycle. But if this had been meant, why would Luke introduce it without explanation?
- It is the first Sabbath of the second month of the year. Again, such a reference is very cryptic.
- The notation links the Sabbaths in Luke chronologically and is a scribal gloss: 4:31 is the first Sabbath, 6:1 is the second Sabbath, and 6:6 is a third Sabbath (though the term ἑτέρῳ [another] is used in 6:6, not the ordinal “third”; Metzger 1975: 139; Fitzmyer 1981: 608; Bovon 1989: 266). However, the events that fall between Luke 4 and Luke 6 are problematic to this solution.
- The phrase alludes to the first Sabbath of Nisan after Passover, which would be the first major Sabbath in the year after Passover and yet would be the second Sabbath of the year. Allusions to this approach are seen in Lev. 23:10–11, 15–16 and at Qumran in 11QTemplea 18.10–19.9. Also, the time of year—harvest time—would be right for such an event. The question is whether such a technical term existed at this time.
Given that the uniqueness of the term in Greek literature, the manuscripts omitting the term, and given that Jerome and his contemporaries did not know what the word meant either, my own tentative view is to see the term as a mistake.