When you say "Marian devotion" most people think of the Rosary, or the Angelus, or any of a myriad of Novenas or daily prayers to Our Lady of Perpetual Help, or Our Lady of the Miraculous Medal, or (my personal favorite) Our Lady of Lourdes.
However, in the Carmelite understanding, this is NOT devotion to Mary. Certainly all of these things are laudable, and truly they show veneration and perhaps even adoration; however, as we understand it, they do not show devotion--at least not the devotion expected from a Carmelite. It is possible to be a very good Carmelite indeed, not say the Rosary at all, and yet be enormously devoted to Our Lady.
The key to Carmelite devotion comes from an adaptation of an old adage, "Imitation is the sincerest form of devotion." True devotion to Mary in the Carmelite sense consists of imitating her. Now, to properly imitate the Blessed Mother AND Sister (Carmelites view her in both roles), one may need sustained reflection on the Rosary or continual dipping into the treasury of prayers of veneration. Too often, though, many of these prayers come as yet one more petition.
What is required is what Pope John Paul the Great wrote in Rosarium Virginis Mariae:
10. The contemplation of Christ has an incomparable model in Mary. In a unique way the face of the Son belongs to Mary. It was in her womb that Christ was formed, receiving from her a human resemblance which points to an even greater spiritual closeness. No one has ever devoted himself to the contemplation of the face of Christ as faithfully as Mary. The eyes of her heart already turned to him at the Annunciation, when she conceived him by the power of the Holy Spirit. In the months that followed she began to sense his presence and to picture his features. When at last she gave birth to him in Bethlehem, her eyes were able to gaze tenderly on the face of her Son, as she “wrapped him in swaddling cloths, and laid him in a manger” (Lk2:7).
Thereafter Mary's gaze, ever filled with adoration and wonder, would never leave him. At times it would be a questioning look, as in the episode of the finding in the Temple: “Son, why have you treated us so?” (Lk 2:48); it would always be a penetrating gaze, one capable of deeply understanding Jesus, even to the point of perceiving his hidden feelings and anticipating his decisions, as at Cana (cf. Jn 2:5). At other times it would be a look of sorrow, especially beneath the Cross, where her vision would still be that of a mother giving birth, for Mary not only shared the passion and death of her Son, she also received the new son given to her in the beloved disciple (cf. Jn 19:26-27). On the morning of Easter hers would be a gaze radiant with the joy of the Resurrection, and finally, on the day of Pentecost, a gaze afire with the outpouring of the Spirit (cf. Acts 1:14).
It is in this never faltering gaze that we most closely join the Blessed Mother. It is in joining her adoration, contemplation, and completion in Jesus Christ that we show her our true devotion. Whenever we address her, she gently but urgently turns our gaze upon her Son, the one without Whom she is not.
For a Carmelite, devotion to Mary is shown by obedience to her example. No number of repeated prayers, no amount of novenas and songs of praise will ever equal joining her, even for a moment, in the loving gaze she lavished and still lavishes upon her precious Son.
True devotion to Mary is becoming like her more and more each day. We become whole in her wholeness--we become real in her gaze upon Jesus. Those things that lead us to joining her are true devotions to Mary, those that do not are laudable prayers, but not the work we are called to as Carmelites. That work is to join the example of our Sister in Carmel and our Mother in the never failing gaze of adoration and love.
That work, as La Madre tells us, is "Mira que tu mira." Look at the One who is looking at you.