Other than the Domine Non Sum Dignus, the Roman Rite (OF/EF) has few pre-communion devotions in the liturgy itself – although the EF also has the Confiteor recited before Communion. If you haven’t any others, the following, taken from Anglican and Eastern Orthodox traditions, are very useful to fill in this gap. There’s usually time to get them done after the invitation and before communion. Your mileage may vary. The first two were used, as well, in the Orthodox Western Rite.
We do not presume to come to this thy Table, O merciful Lord, trusting in our own righteousness, but in thy manifold and great mercies. We are not worthy so much as to gather up the crumbs under thy Table. But thou art the same Lord whose property is always to have mercy: Grant us therefore, gracious Lord, so to eat the flesh of thy dear Son Jesus Christ, and to drink his blood, that our sinful bodies may be made clean by his body, and our souls washed through his most precious blood, and that we may evermore dwell in him, and he in us. Amen. (From the Book of Common Prayer)
I believe, O Lord, and I confess that Thou art truly the Christ, the Son of the Living God, Who camest into the world to save sinners, of whom I am first. I believe also that this is truly Thine own pure Body, and that this is truly Thine own precious Blood. Therefore I pray Thee: have mercy upon me and forgive my transgressions both voluntary and involuntary, of word and of deed, of knowledge and of ignorance. And make me worthy to partake without condemnation of Thy most pure Mysteries, for the remission of my sins, and unto life everlasting. Amen.
Of Thy Mystical Supper, O Son of God, accept me today as a communicant; for I will not speak of Thy Mystery to Thine enemies, neither like Judas will I give Thee a kiss; but like the thief will I confess Thee: Remember me, O Lord in Thy Kingdom.
May the communion of Thy Holy Mysteries be neither to my judgment, nor to my condemnation, O Lord, but to the healing of soul and body. Amen.