In A Textual Commentary on the Greek New Testament, 1974, pp.480, 481, Bruce Metzger explains why "congregation of God" is probably the original reading.
... it is undeniable that theou [of God] is the more difficult reading. The following clause speaks of the church "which he obtained dia tou haimatos tou idiou [with the blood of his own]." If this is taken in its usual sense ("with his own blood"), a copyist might well raise the question, Does God have blood?, and thus be led to change theou [of God] to kuriou [of Lord]. If, however, kuriou were the original reading, there is nothing unusual in the phrase [which would lead the copyist to change it].
Instead of the usual reading of dia tou haimatos tou idiou [with his own blood], it is possible that the writer of Acts intended his readers to understand the expression to mean "with the blood of his Own." (It is not necessary to suppose, with Hort, that huiou [son] may have dropped out after tou idiou [(his) own], though palaeographically such an omission would have been easy.) This absolute use of ho idios [(his) Own] is found in Greek papyri as a term of endearment referring to near relatives. It is possible, therefore, that "his Own" (ho idios) was a title which early Christians gave to Jesus, comparable to "the Beloved" (ho agapetos); compare Ro 8.32, where Paul refers to God "who did not spare tou idiou huiou [his own son]" in a context that clearly alludes to Gn 22.16, where the Septuagint has tou agapetou huiou [the beloved son].
Without committing itself concerning what some have thought to be a slight probability that tou idiou [(his) own] is used here as the equivalent of tou idiou huiou [his own son], the Committee judged that the reading theou [of God] was more likely to have been altered to kuriou [of Lord] than vice versa.