We don't have the rosary in the RC sense, but if I recall correctly the invention of the prayer rope (the precursor to the RC rosary in the sense of the physical beaded chain) is credited to St. Pachomius (292-348), the Egyptian inventor of cenobitic monasticism. I've been told that before its invention, the monks would count their prayers by doing things like dropping pebbles into cups and such. I can't really comment on the OO use of the prayer rope, though, because even though the Copts and Tewahedo both use them, I don't recall having seen one when I was at the monastery of St. Shenouda the Archimandrite.
Since we don't pray the rosary prayers, though, I'm not sure what we would have that is similar. I mean, we pray 41 Kyrie Eleison every hour (of
the Agpeya, the Coptic book of the hours from which we recite our daily prayers), which I guess might be seen as 'repetitive' in a manner similar to the RC prayer, but we don't really think of it that way (just like I doubt Catholics see their rosary prayers that way). And if I remember from RC days, there was also praying of the Hail Mary as part of the Rosary (right? can anyone confirm?). We don't have that prayer either (our "Hail Mary" is a completely different text in Coptic called
Shere Ne Maria that is prayed as part of the Midnight Praises for Sundays), but we have things like the introduction to the Creed which goes:
We exalt you, the Mother of the true Light, and we glorify you, O saint and Theotokos, for you brought forth unto us the Savior of the whole world; He came and saved our souls.
Glory to You, our Master, our King, Christ, the pride of the Apostles, the crown of the martyrs, the joy of the righteous, the steadfastness of the churches, and the forgiveness of sins.
We proclaim the Holy Trinity in one Godhead. We worship Him. We glorify Him. Lord have mercy. Lord have mercy. Lord bless. Amen.
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And we say the Creed a lot (it's again part of every hour of the Agpeya, but also of Matins and Vespers, of the liturgy proper, etc.), so...yeah, it's good. There are lots of prayers we say every day, they're just not necessarily related to whatever other churches are praying or doing, so I'm not sure how to answer the question. I think if the RCs get good spiritual nourishment out of the rosary, then good for them I suppose. There are some issues perhaps from an Orthodox perspective concerning the use of mental imagining or whatever they'd call it in this type of prayer (for the RC rosary's "mysteries", where you're supposed to imagine these particular things related to each day you pray the rosary, in a kind of cycle), but that's why it's their thing and not ours. Rather, on the introductory page for each hour in my English agpeya (where it says "The third hour" or whatever), it says things in the form of "The third hour commemorates Christ's trial by Pilate, His ascension, and the descent of the Holy Spirit" (or whatever the particular hour commemorates), which isn't telling us to imagine any of those things but instead what the prayers, gospel readings, litanies, etc. for the hour are about, which we would be able to understand anyway by...being able to read.
But I guess it gives whoever formatted the English version of the Agpeya that I have something to put on the pages that separate one hour from another, in addition to a nice little Coptic icon-style drawing.
