The general suggestion I have seen for this change is that Stephen (or the author of Acts) has conflated Assyria's conquest of Israel in 722 BC with Babylon's conquest of Judah in 587 BC, effectively summarizing the whole concept of 'exile', and even to highlight the AD 70 destruction of Jerusalem's second temple (similar to what the Babylonians had done).
So Mikael Parsons, Acts, page 100:
Here Luke paraphrases his source, Amos, from "beyond Damascus" to "beyond Babylon" to summarize the history of Israel from the wilderness wanderings to the exile as one of idolatry.
And, more helpfully, F. Scott Spencer, The Gospel of Luke and Acts of the Apostles, page 76:
"Babylon" appears only once in Luke's narratives, but this reference betrays Luke's editorial hand and comes at a strategic point in the story. The long review of Israel's past in Acts 7 includes a citation from Amos 5:25-27, recalling the nation's forty years of wilderness wandering and later exile to a foreign land (Acts 7:42-43). However, otherwise sticking close to his Septuagint source, Luke changes Amos' original destination from "beyond Damascus" to "beyond Babylon," thereby evoking memory of the temple's destruction and the Babylonian exile. By incorporating this into Stephen's speech (7:2-55), where he responds to charges of speaking against "this holy place" (temple) and predicting its demolition (6:13-14), Luke draws a subtle link between the Babylonian and Roman assaults on the Jerusalem temple in the sixth century B.C.E. and first century C.E., respectively.