The Church offers us different prayers that we can say every day of the week for the faithful departed. These are especially useful for offering a novena on behalf of the dead, or for praying during those seasons of the year (November, in the Western Church; Lent, in the Eastern Church) designated by the Church as times of fervent prayer for the dead.
This is a prayer for the faithful departed to be offered on Sundays.
Sunday Prayer for the Faithful Departed
O Lord God omnipotent, I beseech Thee by the Precious Blood, which Thy divine Son Jesus shed in the Garden, deliver the souls in purgatory, and especially that one which is the most forsaken of all, and bring it into Thy glory, where it may praise and bless Thee for ever. Amen.