When (at age 8 in 1946) I received my brown scapular, I was standing. I attended that ceremony many years later, so the picture is clear: the candidates stood, the carmel;ite priest put the scapular to their shoulder and blessed them.
Here is the prayer, on that time this was in Latin
English
Priest - Show us, O Lord, Thy mercy.
Respondent - And grant us Thy salvation.
P - Lord, hear my prayer.
R - And let my cry come unto Thee.
P - The Lord be with you.
R - And with your Spirit.
P - Lord Jesus Christ, Savior of the human race, sanctify + by Thy power these scapulars, which for love of Thee and for love of Our Lady of Mount Carmel, Thy servants will wear devoutly, so that through the intercession of the same Virgin Mary, Mother of God, and protected against the evil spirit, they persevere until death in Thy grace. Thou who livest and reignest world without end. Amen.
THE PRIEST SPRINKLES WITH HOLY WATER THE SCAPULAR AND THE PERSON(S) BEING ENROLLED. HE THEN INVESTS HIM (THEM), SAYING:
P - Receive this blessed scapular and beseech the Blessed Virgin that through Her merits, you may wear it without stain. May it defend you against all adversity and accompany you to eternal life. Amen.
AFTER INVESTITURE THE PRIEST CONTINUES WITH THE PRAYERS:
P - I, by the power vested in me, admit you to participate in all the spiritual benefits obtained through the mercy of Jesus Christ by the Religious Order of Mount Carmel. In the name of the Father + and of the Son + and of the Holy Ghost. + Amen.
May God Almighty, the Creator of Heaven and earth, bless + you, He who has deigned to join you to the Confraternity of the Blessed Virgin of Mount Carmel; we beseech Her to crush the head of the ancient serpent so that you may enter into possession of your eternal heritage through Christ our Lord.
R - Amen.
THE PRIEST THEN SPRINKLES AGAIN WITH HOLY WATER THE PERSON(S) ENROLLED.