Having chased up the account provided in the answer that follows, I now find there is a full-blown and properly specialist study of precisely this question. Gratifyingly, the main contours are the same, and it looks like Benecke is indeed one of the "heroes" of the tale. Interested readers should therefore consult: Benjamin Schliesser, "‘Exegetical Amnesia’ and ΠΙΣΤΙΣ ΧΡΙΣΤΟΥ: The ‘Faith of Christ’ in Nineteenth-Century Pauline Scholarship", Journal of Theological Studies 66.1 (2015): 61-89 for wider context, full details, further references (including patristic resources) and informed discussion.
So far as I'm aware, the first argument for the "subjective genitive" (something like "the fidelity of Christ") rather than the commmon understanding as the "objective genitive" (something like "faith in Christ") for Πίστις Χριστοῦ (pistis christou) appears in the Romans commentary of Wilhelm Benecke, Der Brief Pauli an die Römer (Heidelberg, 1831), pp. 69ff. = An exposition of St. Paul's Epistle to the Romans (Longman et al, 1854), pp. 142ff. It is a clear, non-technical explanation of and plea for the "subjective genitive". Benecke was not a professional theologian: he is best known for a work on marine insurance! The preface to the English translation of his Romans commentary gives a full biography supplying the background for his foray into theological commentary.
Benecke was followed by J.P. Lange, Der Brief Pauli an die Römer (2nd edition; Velhagen und Klasing, 1868; first published 1865), p. 84 = Lange and F.R. Fay, The Epistle of Paul to the Romans (Scribners, 1869), p. 129. Lange chides contemporary interpreters for failing to reckon with Benecke's arguments.
Another 19th C. proponent is Johannes Haussleiter, Der Glaube Jesu Christi und der christliche Glaube: Ein Beitrag zur Erklärung des Römerbriefes (= The Faith of Jesus Christ and the Christian Faith: A Contribution to the Exposition of Romans), published in 1891 by Georg Böhme (Verlag). He is credited with challenging "the hitherto almost universally accepted view" by Sanday & Headlam, in their older ICC commentary on Romans, pp. 83-84, who summarize and reject his view.1
George Howard wrote a useful article addressing OP's interests (drawing attention to Lange & Fay along the way). He supports the "subjective genitive" interpretation in his article "On the 'Faith of Christ'", Harvard Theological Review 60/4 (1967): 459-465. In it he argues that the Syriac Peshitta unambiguously uses the subjective genitive, and that the Gal. 2:16 occurrence in particular almost demands it.
Howard claims in turn (p. 461) that the "objective genitive" -- almost ubiquitous in more recent writing -- has its origins with Luther. I have checked Luther's Romans and Galatians commentaries, and can't see any special interest in the phrase there (although his remarks on Gal. 3:26 come close, still without explicitly rejecting a "subjective" construal). Howard appears to be basing his comment on Luther's translation practice, though, and Luther's Works are voluminous enough that it might be in there somewhere.
At any rate, this is enough to make clear that the "subjective genitive" understanding goes back at least into the 19th C -- 1831 the first clear expresssion (so far found!) -- and possibly earlier if Howard is correct.
- Having posted this answer, I see that the Hays volume referenced by OP also has a discussion of this issue, noting contributions by both Haussleiter and Howard -- although different than the ones cited here! Here Hays is in need of supplementing, and this may be another one of those places where somehow academic tradition enshrines a faulty memory: clearly Haussleiter was not the first to argue for the subjective genitive, even in the 19th C.
HT: @Nathaniel for help tracking down Lange's German commentary.