I would like to know if there is a way to do such a thing in the Byzantine rite. Or is the only option to actually pray the Hours?
The prayerbooks for the laity contain selections from Vespers and Matins:
Vespers:
Psalm 103
Psalm 1 (Sunday and Feasts only)
Psalm 141
Psalm 140
Psalm 129
Psalm 116
O Joyful Light
Vouch Safe O Lord
The Canticle of Simeon
Matins:
Psalm 3
Psalm 37
Psalm 62
Psalm 87
Psalm 102
Psalm 145
The Polyeleos (Sunday and Feasts only)
The Evlogitaria (Sunday Only)
The Gradual Hymn First Antiphon Tone 4
Hymn of the Resurrection (Sunday Only)
Canticle of the Theotokos
Psalm 148
Psalm 149
Psalm 150
The Great Doxology (Sunday and Feasts only)
The Doxology (weekdays)
as well as the complete text for Compline.
This is the closest the Byzantine tradition comes to offering a reduced schema of the Divine Office for the laity. Since the Divine Office always remained a public liturgical service, as opposed to a personal obligation of clerics, there was never any thought given to rearranging it for private recitation for anyone, cleric or layperson. As already mentioned , in monasteries the Jesus Prayer was assigned to make up missed services.
According to Fr. Lev Gillet (A Monk of the Eastern Church):
“The Greek rosary (komvoschinion or tchotki) is made up of 100 pearls or wooden beads or knots of wool or thread. The practice is to make one rosary bead and one metanoia correspond to each Jesus Prayer. There are two kinds of metanoia: the lesser metanoia, a deep bow without bending the knees; and the greater metanoia or full prostration, with the forehead touching the ground. On Mount Athos, 1,200 (12 x 100) greater metanoias are made every day, and in the evening 300 lesser metanoias. The Jesus prayer has two forms. The ordinary one is very full: ‘Lord Jesus Christ, Son and Word of the living God, through the prayers of thy most pure Mother and of all the Saints, have mercy on us and save us.’ The shorter form, ‘Lord Jesus Christ, Son of God, have mercy on me,’ is considered a penitential prayer. The Russian usages are different. The Russian rosary is composed of 107 knots divided in this way: 1 large knot and 17 small knots, 2 large knots and 33 small knots, 1 large knot and 40 small knots, 1 large knot and 12 small knots. These four divisions represent the four parts of the daily office: Vespers, Compline, Matins, and the prayers called ‘Typika’. The Russians use the formula: ‘Lord Jesus Christ, Son of God, have mercy on us.’ They make fewer metanoias than the Greeks. In their use of the rosary, they begin with 10 greater metanoias, next 30 lesser metanoias (both accompanied by the Jesus Prayer); then the Jesus Prayer is said 60 times without metanoias; on the remaining knots great metanoias are made. The rosary should be said 5 times a day. The Russian equivalents between the Jesus Prayer (with metanoias at each invocation) and the office are: for Vespers, 500; for Compline, 200; for Matins, 500; for the Typika, 700. One sees that the practice is somewhat severe.”
From: A Monk of the Eastern Church (Lev Gillet), The Jesus Prayer (New York: St Vladimir’s Seminary Press, 1997), fn. 8, p. 72.