Gospel Guidebook: Getting and Keeping It Right 
Exegetical Problems of "Faith of Jesus Christ" Subjective Genitive
Exegetically speaking, the subjective genitive translation "faithfulness of Christ" in Romans 3:22 has problems. It is often pointed out that Romans 3:3 refers to the "faithfulness of God," and this is true, but this verse is far removed from Romans 3:22. Also, the context is completely different. Romans 3:3 refers to the "faithfulness of God" in the context of Him bringing wrath. Likewise, the "righteousness of God" in Romans 3:5 is in the context of God judging the world. These instances of God's faithfulness and righteousness don't fit the narrative suggested by those who tell us that "covenant faithfulness" and "faithfulness of Christ" refer to God's salvific activity in the world.
In the immediate context of Romans 3:22, we are definitely presented with the faith of the believer, and this is consistent with the faith of the believer in the thematic verses of Romans 1:16-17. This context and backdrop support the objective genitive translation "faith in Christ."
Also, if Paul does intend to teach the "faith(fulness) of Christ" in Romans 3:22, then it is surprising that he never unpacks this ambiguous statement. In the context, we learn that we are justified by the death of Christ in His blood (Romans 3:25 and later in Romans 5:6-10), but if this is all that the "faith(fulness) of Christ" means, then it is totally consistent with Protestant theology and it doesn't permit speculation such as "Christ's faithfulness being implanted in us to create ontological transformation and achieve justification through a lifetime of good works." The word pistis (i.e., faith) does not even appear once in Romans 6 to 8, so Paul's discussion on sanctification in those chapters is certainly not meant to unpack the meaning of the phrase "faith(fulness) of Christ." And yet, the opponents of Protestant theology insist that those chapters consist of the heart and soul of the gospel.
Commenting on this issue, Moises Silva said the following in Volume 3 of the New International Dictionary of New Testament Theology and Exegesis (see especially page 769):
With regard to the debate as a whole, I happen to believe, naively perhaps, that the evidence is not all that ambiguous—or to put it more accurately, that the ambiguities in the data are plainly resolved by Paul's many unambiguous statements. If by pistis Christou (which in isolation can indeed signify any number of things) the apostle had meant either "Christ's faith" or "Christ's faithfulness," it would have been ridiculously easy for him to make that point clear beyond dispute. Among various possibilities, he could have, for example, indicated—in the same contexts—one or two ways in which Jesus believed and how those acts of faith were relevant to the matter at hand. Or he could have told us—again, in the same contexts—that his message of dikaiosyne ("righteousness, justification") is true because Christos pistos estin ("Christ is faithful"). What could have been simpler? And considering the theological importance of this issue, one would think that he might have made a special effort to clarify matters.
Instead, if some scholars are to be believed, Paul did not have enough sense to realize that the phrase pistis Christou is ambiguous. And to make matters worse, he unwittingly misled his readers by using the verb pisteuo with Christos as direct object again and again in the very same passages that have the ambiguous phrase! His bungling proved spectacularly successful, for in the course of nearly two millennia, virtually every reader—including ancient scholars for whom Greek was their native language—understood the phrase to mean "faith in Christ" and gave no hint that it might mean something else.