The precise dating of Boiardo's Tarot poems, Viti's commentary, and the woodcut deck that was eventually produced, are open questions. Some discussion of the first question, dating the poems themselves, took place on the Boiardo mailing list in 2003. Ross was kind enough to invite me to read the archived posts: the evidence and arguments presented seem to agree with each other, suggesting that Boiardo's Tarocchi were probably written in the early 1460s, around 1463.
Ross Caldwell reported that Rudolfo Renier proposed an early date, perhaps 1461, because of the "juvenile" nature of the poems; Vittorio Rossi suggested 1469-78, based on Boiardo's close relations with the d'Este court at that time, but, as discussed below, those close relations appear to have begun in 1462; Simona Foa suggested that Boiardo wrote it while at a time when the passion for Tarocchi was high. Caldwell noted that "this is not helpful to us, unfortunately, because the passion for tarocchi and other card games remained relatively constant with the Este."
Raimondo Luberti reported that both Rodolfo Renier and Giovan Battista Venturi considered Boiardo's Tarocchi a juvenile work, and that he was, at the time he composed it, a struggling and insecure poet, still not able to manage his rhymes well. Luberti wrote, "His verses were experimental and under obvious influence of French Romances (Tristan, etc.) and especially of Petrarchism also for the argument (idealized Love, etc.) Later, in Orlando, he was under the influence of more relatively modern poets such as Pulci and the others XV century authors prose and poetic authors."
In addition to the immature character of the writing, there is also the triviality of the form being exploited, a card game, and the commonplace nature of the development of the subject, selecting famous exemplars for the Passions of the Soul. These both suggest that the Tarocchi was a youthful exercise. Then there is Duke Borso, Sigismondo, and Ercole's fondness for cards, and specifically Tarot, referred to by Caldwell. Even if this was a constant, it suggests an argument for narrowing the time frame, as indicated by Rossi. Matteo Maria Boiardo was born in 1441. Mari Hoshizaki, referencing Gardner's Dukes and Poets in Ferrara, described for the mailing list Boiardo's "coming of age" and early relations with the rulers of Ferrara. Here are the key passages from Gardner.
In February, 1460 -- on the death of Giulio Ascanio -- he first comes forward as the feudal Lord, Comes Scandiani et Casalgrandis, in a letter to Count Silvio di San Bonifazio, Captain of Reggio, announcing the death of his uncle....
Boiardo appears to have passed the next eight or nine years of his life mainly at Scandiano, in the midst of the scenery he so loved, playing the part of a feudal lord, hunting and entertaining, and much engaged in the somewhat prosaic affairs of the waters of the Secchia -- a standing source of contention between the Boiardi and the Commune of Reggio, which that latter city derived its water supply from a canal from that stream....
Although high in favour with the Duke, whose benign bearing towards him he records in one of his sonnets, a far warmer devotion united Boiardo with Ercole d'Este. After the recall of the latter from Naples in 1462 and his appointment as ducal governor of the Duchy of Modena, Boiardo was a constant visitor to the latter city, as also to the smaller Court that Sigismondo held in Reggio.
(Edmund G. Gardner. Dukes and Poets in Ferrara: A Study in the Poetry, Religion and Politics of the Fifteenth and Early Sixteenth Centuries, 1904; 255-6.)
According to that account, Boiardo was quite close to Ercole, and from 1462 was a "constant visitor". Given Caldwell's observation that the d'Este "passion for Tarocchi" was a constant, Boiardo would certainly have been exposed to that during his many visits from the early 1460s. This would have been the period in which that passion was most striking to him, and in which he would have been most likely to cater to it in some extravagant manner. Thus, the argument from the trivial subject matter and commonplace development (alluded to in the previous post) agrees with the argument from the immature execution which agrees with the argument from Boiardo's first close and protracted contacts with the d'Este passion for Tarocchi.