Jim, I'm not sure if this is what you are looking for, but in De Musica Sacra, promulgated in 1958, at the end of the pontificate of Pope Pius XII, there is some mention of vernacular hymns at the Low Mass and the Sung Mass:

14. a) In sung Masses only Latin is to be used. This applies not only to the celebrant, and his ministers, but also to the choir or congregation.

"However, popular vernacular hymns may be sung at the solemn Eucharistic Sacrifice (sung Masses), after the liturgical texts have been sung in Latin, in those places where such a centenary or immemorial custom has obtained. Local ordinaries may permit the continuation of this custom 'if they judge that it cannot prudently be discontinued because of the circumstances of the locality or the people' (cf. canon 5)" (Musicæ sacræ disciplina: AAS 48 [1956] 16-17).

b) At low Mass the faithful who participate directly in the liturgical ceremonies with the celebrant by reciting aloud the parts of the Mass which belong to them must, along with the priest and his server, use Latin exclusively.

But if, in addition to this direct participation in the liturgy, the faithful wish to add some prayers or popular hymns, according to local custom, these may be recited or sung in the vernacular.

There is more on vernacular hymns in Musicae sacrae disciplina (1955):

62. As We have said before, besides those things that are intimately associated with the Church's sacred liturgy, there are also popular religious hymns which derive their origin from the liturgical chant itself. Most of these are written in the language of the people. Since these are closely related to the mentality and temperament of individual national groups, they differ considerably among themselves according to the character of different races and localities.

63. If hymns of this sort are to bring spiritual fruit and advantage to the Christian people, they must be in full conformity with the doctrine of the Catholic faith. They must also express and explain that doctrine accurately. Likewise they must use plain language and simple melody and must be free from violent and vain excess of words. Despite the fact that they are short and easy, they should manifest a religious dignity and seriousness. When they are fashioned in this way these sacred canticles, born as they are from the most profound depths of the people's soul, deeply move the emotions and spirit and stir up pious sentiments. When they are sung at religious rites by a great crowd of people singing as with one voice, they are powerful in raising the minds of the faithful to higher things.

64. As we have written above, such hymns cannot be used in Solemn High Masses without the express permission of the Holy See. Nevertheless at Masses that are not sung solemnly these hymns can be a powerful aid in keeping the faithful from attending the Holy Sacrifice like dumb and idle spectators. They can help to make the faithful accompany the sacred services both mentally and vocally and to join their own piety to the prayers of the priest. This happens when these hymns are properly adapted to the individual parts of the Mass, as We rejoice to know is being done in many parts of the Catholic world.

Apparently for quite a long time Greek liturgy was in use in certain cities of the Italian peninsula well after the fall of the western Empire and into the Byzantine period, even as late as the split of 1054 it seems to have been common in some places according to a few sources. As far as liturgical law goes, though, the question is what was in use during the 200 years up to the council of Trent?

Generally speaking we are not free to borrow from other Rites (liturgically), so a liturgical Greek hymn of Byzantine rite origin could not just be freely grafted into the Roman rite unless there was a tradition in support of that particular usage (such as a long established local custom). (Now with the wider latitude in music you could do so, but in the period between Trent and Vatican II it would have been problematic it seems.)