Andrew Perry argues that the "tabernacle of David" in Amos 9/Acts 15 refers to a physical structure (i.e., a temple).
Andrew Perry, “Eschatological Deliverance: The Spirit in Luke-Acts” (PhD Thesis; Durham University, September 2008), 273-75
Scholars have argued variously that the expression “tabernacle of David” refers to the restoration of Israel, the nascent church, and Jesus. Chance argues that Luke expects the restoration of Jeruslaem, but on the question of a restored temple he avers, “given the close association between the city and temple thought Luke-Acts, one might offer a positive answer, though with great reserve.”
R. Bauckham has recently analysed Luke’s citation from the point of view of Luke’s source and Luke’s own design. He notes that the building term, ἀνοικοδομέω, replaces the two instances of ἀνίστημι in the LXX of Amos, and affirms, “they would not have been made had the exegete who produced this form of the text not wished it to be quite clear that the reference is to the restoration of a building”. He supports this argument with the claim that the omission of καὶ άνοικοδομήσω τὰ πεπτωκότα αὐτῆς from the citation of Amos was made because this phrase suggests the rebuilding of city walls rather than a temple.
After reviewing second Temple texts which refer to the eschatological temple being built by God or his agent, Bauckham concludes, “Thus the exegete whose work is embodied in Acts 15:16-18 may have understood the phrase σκηνή Δαυίδ to mean God himself will build the eschatological temple miraculously through the agency of the Davidic Messiah, though he may simply have taken it to refer to the Temple of the Messianic age, which God will build when ‘David’ rules God’s people”.
Bauckham further argues that “In a Jewish Christian context in which Amos 9:11-12 is understood to predict the inclusion of Gentiles in the eschatological people of God, it is clear that the eschatological Temple must be understood as the Christian community”. His evidence is based on texts outside Acts and he shows that “the Temple as the community” was a prevalent idea in early Christianity. His point is that scriptural prophecies of the Gentiles coming to worship God were seen to be fulfilled in them joining the Christian community. While Chance has shown that the idea of the Christian community as the eschatological temple is not prevalent in Luke or Acts, Bauckham points to Acts 15:16 as evidence that Luke saw the community in this way. We conclude, following Bauckham, that the speech of James is therefore part of Luke’s temple-directed apologetic.