In his 1985 book The Tarot Trumps, John Shephard reproduces a 1488 Venetian engraving of the Triumph of Love from Petrarch's Trionfi.
The inspiration for including Pope Joan in the Trionfo d'Amore must have been Boccaccio's De Mulieribus claris (Famous Women). Boccaccio attributes her career (the cause of both her rise and downfall) to Love and Learning (Venus and Minerva) -
According to some, while a young girl she was beloved by a certain young student, whom she also loved; and so ardently, that disregarding the fact that she was a maid, putting aside all feminine timidity, she secretly left the home of her father and followed her lover all the way to England, having changed her clothing and her name; and there, in his company, she studied letters, being supposed by everyone to be a (male) student, while nevertheless at the same time being given as much to the studies of Venus as to those of Minerva. Afterwards, the young man being dead, when she had come to know how intelligent she was, attracted by the pleasure of learning, and remaining in the same manner of dress, she wanted no more to be somebody's companion, nor to be known as a woman but instead she continued assiduously at her studies, and had profited so much by study of the liberal arts, and at the study of holy letters, that she was reputed to be more excellent than all the other students....
(after going to Rome and becoming Pope, she gives birth after three years...)
... by this means the fraud became clearly apparent, for how long she had deceived every other man, except for her lover.
Many such engravings were based on manuscript illuminations, and it would be interesting to see if there is an earlier painted manuscript with this figure in it.
I found a possible painted precursor to the 1488 image. Unfortunately I have only a black-and-white image which can't resolve much detail.
(Triumph of Love from a Venetian printed edition of 1478, with painted illustrations from c. 1480 (taken from J.B. Trapp, "Illustrations of Petrarch's "Trionfi" from Manuscript to Print and Print to Manuscript" (1999) reprinted in Studies of Petrarch and His Influence (Pindar Press, 2003) fig. 10.)
This is apparently the first printed edition of the Trionfi, with the second known one being the 1488 edition noted in the first post on this thread. The 1488 edition also includes the first engraved images of the Trionfi.
You can see the cardinal(s ?) and bishop behind the Popess, all figures also included in the 1488 edition. It's not as clear the figure is a Popess as it is in the 1488 version.
Sorry I can't do better at the moment. This image is not published in color or high quality anywhere I can find yet.