The idea that the Proper chants are somehow rite-specific is a modern imposition, in a "picking appropriate hymns" sort of way. Rather, as Dr. Mahrt has pointed out, they tend to be congruent within their various cycles. Just as very few Offertory chants speak directly about offering, so the Communion chants are quite often not directly related to "taking communion". In the modern Missal, the ABC-specific chants tend to coordinate with the Readings, and the Communion chants that set Gospel texts are usually from the Gospel of the day.

Of course, you are welcome to use one of the seven ad libitum Communion chants (Graduale Romanum 1979, p. 391), which are all Body and Blood-related.

Useful thoughts in Discussion 1705 ...
http://musicasacra.com/forum/comments.php?DiscussionID=1705

One of the deep principles of singing the Mass is that what we sing as we process to communion are words taken from the gospel of the day. Why? Communion is the fruit of the proclaimed word!

from the Praenotanda of the Graduale Simplex §21

. . . any version of Psalm 34 (I will bless the Lord), with or without antiphon “Taste and see . . . ” (“Alleluia” may be used as the antiphon outside of Lent), or Psalm 23 with the antiphon “I am the living bread” (add “alleluia” outside of Lent) or the Magnificat with the antiphon “My soul glorifies his holy name” or the hymn “Ubi Caritas est vera”

from the Ordo Cantus Missae [OCM], the Praenotanda of the Graduale Romanum

“ . . . the new plan of biblical readings required transferring a number of texts (for example, communion antiphons) to other days more closely connected with the readings.” [OCM ¶1]

“ . . . chants closely related to the readings should, of course, be transferred for use with these readings.” [OCM 19]

See James W. McKinnon, The Advent Project: The Later Seventh-Century Creation of the Roman Mass Proper (Berkeley, CA: The University of California Press, 2000; 0-520-22198-2), 326–355, for his discussion of the genius and genesis of the gospel-communion.

The following, then, are the principles:

(1) Of the 163 communion songs of the Roman Gradual only eight songs refer to the Body and Blood of Christ. All of these songs were realigned as a consequence of our new lectionary so that, as OCM 19 says, "chants closely related to the readings should, of course, be transferred for use with these readings."

(2) Of the sixty-two communion songs of the Simple Gradual, only four songs refer to the Body and Blood of Christ.

(3) Of the 618 communion songs of the Sacramentary, only sixty-eight songs refer even indirectly to the Body and Blood of Christ.

Why this infrequency? Because communion is about more than the real presence of Christ's Body and Blood. It is about how this Food and Drink is meant to forgive our sins, restore us to community, and to prepare us for life eternal, among many other things. (O sacrum convivium, in quo Christus sumitur, recolitur memoria passionis ejus, mens impletur gratia, et futurae gloriae nobis pignus datur. “O holy banquet in which Christ is consumed, the memory of his passion is recalled, the mind is filled with grace, and a pledge of future glory is given to us.” St. Thomas Aquinas, Canticle Antiphon for the Second Vespers of Corpus et Sanguinis Christi.)

Because communion is the fruit of the proclaimed word, especially the gospel, the communion song ideally “quotes” the proclaimed word, especially the gospel. It must be at least seasonally relevant, long enough and interesting enough to bear the weight of repetition. Its style needs to be processional (more inspiring of movement than of meditation) and responsorial (sharing the burden of the text and music alternately, between the assembly and the cantor, choir, or instruments). Its texts need to have a biblical density and richness to it so that it can reflect as fulfillment what the Liturgy of the Word announced as promise.