If the question is "Who is the referent of Daughter Zion", the answer is: Those who believe in the Lord (then and especially in the NT age). How so? Let's look at the passages that speak about this Daughter Zion and this humble/conquering king:
“<9> Rejoice greatly, Daughter Zion! Shout in triumph, Daughter Jerusalem! Look, your King is coming to you; he is righteous and victorious, humble and riding on a donkey, on a colt, the foal of a donkey. <10> I will cut off the chariot from Ephraim and the horse from Jerusalem. The bow of war will be removed, and he will proclaim peace to the nations. His dominion will extend from sea to sea, from the Euphrates River to the ends of the earth. <11> As for you, because of the blood of your covenant, I will release your prisoners from the waterless cistern. <12> Return to a stronghold, you prisoners who have hope; today I declare that I will restore double to you.” (Zechariah 9:9–12 CSB17)
We take note of two details:
- The kingdom of this king will be massive. Notice the expanding character of this kingdom: Jerusalem --> sea to see --> ends of the earth (”עַד־אַפְסֵי־אָֽרֶץ“ (Zechariah 9:10 BHS-T))
- This king pays for sin “double to you.” (Zechariah 9:12 CSB17). This is a clear parallel to Isaiah 40, where the Lord pays down double to ensure their sins are covered and paid for.
The interpretation that fits this description is those who believe in the Lord (both in the OT and in the NT age)
But there are more passages to consider:
“<14> Sing for joy, Daughter Zion; shout loudly, Israel! Be glad and celebrate with all your heart, Daughter Jerusalem! <15> The LORD has removed your punishment; he has turned back your enemy. The King of Israel, the LORD, is among you; you need no longer fear harm.” (Zephaniah 3:14–15 CSB17)
Notice, that in Zephaniah, this king has ...
- Turned aside the judgment against them (הֵסִ֤יר יְהוָה֙ מִשְׁפָּטַ֔יִךְ)
- Turned away their enemy (פִּנָּ֖ה אֹֽיְבֵ֑ךְ)
The greatest enemy of us all has always been the Devil. While this is not the only enemy of believers in the Lord, he definitely tops the list. So also, the just judgment that could have been leveled against believers is now turned away in Christ.
Finally, we consider one last passage:
“<10> “Daughter Zion, shout for joy and be glad, for I am coming to dwell among you”—this is the LORD’s declaration. <11> “Many nations will join themselves to the LORD on that day and become my people. I will dwell among you, and you will know that the LORD of Armies has sent me to you. <12> The LORD will take possession of Judah as his portion in the Holy Land, and he will once again choose Jerusalem. <13> Let all humanity be silent before the LORD, for from his holy dwelling he has roused himself.”” (Zechariah 2:10–13 CSB17)
Notice how God's word broadens the scope of who "Daughter Zion" is. Daughter Zion is describes as...
- "Many nations will be joined to the Lord." (”וְנִלְווּ֩ גוֹיִ֨ם רַבִּ֤ים אֶל־יְהוָה֙“ (Zechariah 2:15 HMT-W4))
- "And they will be for me a people." (”וְהָ֥יוּ לִ֖י לְעָ֑ם“ (Zechariah 2:15 HMT-W4))
Here we have a united people gathered from an abundance of nations. We have a strong parallel in Revelation:
“And they sang a new song, saying: “You are worthy to take the scroll and to open its seals, because you were slain, and with your blood you purchased for God persons from every tribe and language and people and nation.” (Revelation 5:9 NIV11-GKE)
Summary: Daughter Zion = Believers of all ages who believe in the Lord. However, this is especially fulfilled both in Jesus' entry into Jerusalem on Palm Sunday and his final return on Judgment Day.
"Daughter of Zion" (bat tzion) is phrase that does not lend itself to a one-size-fits all definition. The term appears many times in the Hebrew Bible, sometimes referring to God's faithful people and other times to his beloved but fallen nation. (Isaiah 3:16, Jeremiah 8:19, Micah 1:13) In some case it clearly refers to the nation rather than its women and is better translated "Daughter Zion." It appears only once in the New Testament. In this case, as the OP suggests, it harkens back to prophecy of Zechariah.
Matthew 21:5
Say to daughter Zion, ‘Behold, your king comes to you, meek and riding on an ass, and on a colt, the foal of a beast of burden.’
However, even in this case "daughter of Zion" is not a reference to Christians. Rather it refers to the people to people to whom the Messiah was initially sent. Here, Zion also carries the connotation of Mount Zion, Jerusalem's highest hill, very close to the spot where Jesus entered the Temple on "a donkey's colt. Based on the NT, Christians can rightly claim to be the New Israel, but Zechariah's prophecy does not refer only to those who accepted Jesus as king; it refers to those who are urged to rejoice in the king's coming. As we know from the gospels not all of those invited to share in the King's joy at the wedding banquet of his Son actually responded to the invitation. (Matthew 22:2)
Conclusion: Even if we limit the discussion to the prophecy of Zechariah, the OP's suggestion that 'Daughter of Zion' refers only to Christian believers cannot be sustained, because the proclamation of Jesus as king was made not only to believers but all who could hear it. Moreover, Zechariah's prophecy cannot be divorced from the dozens of other uses of the term in the Bible, in which it refers both to God's faithful people and to his beloved but rebellious "daughter."