I suspect that in the various OO traditions, the basic "prayer rule" is the canonical hours. At least this is the case in the Syriac tradition. The canons on prayer contain references to prayer twice, thrice, or seven times daily as an obligation for clergy and laity; most likely, this reflects the gradual development of the daily office, and the way this has been reconciled is to pray the seven hours in groups of two (evening and morning) or three (evening, morning, and noon) daily.
Outside of Sundays, feasts, Lent, and Holy Week, the daily prayers are in the Book of Common Prayer (Ktobo Daslutho Shehimto
, not the Anglican service book of the same name), a one week cycle of seven daily offices composed mainly of fixed psalmody and/or hymnography. The "monastic" hours are chanted according to the tone of the day, while the "cathedral" hours have an assigned tone that never changes. One can sing all seven offices daily on one's own as done in churches, but there are ways to ease the "burden" (e.g., reading instead of chanting). There are also some "traditional" ways of abbreviating the hymnography so that a one week cycle becomes a two week cycle, and there's less text to get through daily.
That's still a lot of prayer.
When I asked my bishop about the "obligation" of praying the hours, he told me it was binding on clergy and laity, but that the Trisagion, recited at the beginning and end of each hour, was the "core", and so the basic obligation could be fulfilled in a pinch by the Trisagion prayers and the Creed. Many abbreviated prayer books for the laity use this convention, and so the "evening" and "morning" prayers are basically the Trisagion so many times, with some of the fixed psalms, prayers, and hymns of the major hours.
Most people use some form of the latter because it's easiest, but there is a growing movement toward the fuller office (and it's coming from the younger generations!). There are, of course, people who find fixed schemes of prayer "boring' and so they do their own thing for "prayer time", but usually they're not getting that from their confessor, but from Evangelicalism.
Personally, I try to stick to the daily offices; when I don't have my own words, the Church gives me words, and when I have my own words, I can still pray with the rest of the Church. I fail a lot in practice; most mornings are a disaster--without coffee and some time to recover from the stress of having to wake up, I can barely summon the required concentration for one Trisagion.
But the day and evening hours are manageable if I am disciplined.
In addition to the daily office, my confessor has advised me to cultivate "personal prayer" by the use of the Jesus Prayer, the reading of Scripture, and prayer in my own words; he left the "how" and "when" to me, so I've had the freedom to figure out what works best. Liturgical prayer feeds our personal prayer, and the relationship we cultivate with God through private prayer enriches our liturgical prayer, making "prayers out of a book" genuinely our own prayer. But honestly, sometimes it's easier to take the "Trisagion shortcut" for the offices and focus more on "personal" prayer (and another trusted counselor has told me that, in certain circumstances, it may be preferable to put aside the canonical hours in favour of this type of prayer). The Jesus Prayer, our own individual prayers, the Psalms, all of these are also found in our tradition and encouraged.
It's good to have a confessor or spiritual father in order to help figure out a game plan that we can stick with; it's also useful to keep in touch with him regarding how it's working out, whether modifications are in order, our own failings, etc. My confessor hears a lot about my laziness and failures in prayer, but he is kind and helps me get back on track. Many have such a person in their lives, but for others confession is, sadly, more of an annual requirement, and so who knows what gets covered when it comes to these sorts of issues.