This year, Corpus Christi falls on the same day as the Visitation of the Blessed Virgin Mary to Elizabeth, so the latter is transferred to 1st June.
The readings for Corpus Christi are:
1 Corinthians 11:23-26
In Genesis, King Melchizedek of Salem brings out bread and wine, and blesses Abram, who gives him one tenth of everything.
The portion from Psalm 116 is about how to repay the Lord for his bounty and goodness: the psalmist commits to lifting up the cup of salvation, paying vows to the Lord in the presence of his people, serving God and offering a thanksgiving sacrifice.
1 Corinthians is about the institution of the Lord’s Supper.
John 6:51-58 is Jesus saying he is the Bread of Life, but he doesn’t mean ordinary life but eternal life: “Those who eat my flesh and drink my blood have eternal life, and I will raise them up on the last day; for my flesh is true food and my blood is true drink. Those who eat my flesh and drink my blood abide in me, and I in them.”
This feast is about the Body of Christ as present in the sacrament of Holy Communion, in the bread and the wine; or about thanksgiving for said sacrament, if the Real Presence makes you theologically uncomfortable — but it’s also about the Church as the Body of Christ.
My own SATB setting of Christ Has No Body Now On Earth But Ours, words attributed to Teresa d’Avila, would be appropriate for this — and also might work well for the first Eucharist of new priests ordained at Petertide, which isn’t so very far off. You can listen to a demo recording of it on Youtube, and download it from the Choral Public Domain Library.
If you want something a little more traditional, there is quite a bit to work with!
O Salutaris Hostia is one traditional text for Corpus Christi.
There’s a setting by Mel Bonis for four voices and organ, but you’ll have to scroll or search the page it’s listed on to find it, and as the O is typed as a 0 it isn’t that easy to find!
And, of course, a good Ave Verum Corpus always works for Corpus Christi. Here’s one by Andrea Ramsey.