From my research Christians of the Byzantine tradition will use a prayer rope consisting of anywhere from 33 to 300 knots. It may be divided up with beads, but the divisions will vary according to what customs one follows (Russian, Romanian, Greek, etc.). The Russians also use a leather “chaplet” known as a Lestovka. This is something one commonly sees among Old Believers, but is not completely unknown by the rest of Byzantine Christianity.
Coptic Christians also often use prayer ropes, but one may find them using a “mequtaria” as well. The mequtaria is a prayer rope, but the prayers said on it are different and the way the knots/ beads are divided is also different.
Ethiopian Christians will use a mequtaria and/or some form of walking stick with notches carved into it.
Maronites will will typically pray the Latin/Dominican rosary, but one may see a Maronite praying the Jesus Prayer on a prayer rope from time to time. (Incidentally there is a wonderful little pamphlet that promotes a “Maronite rendition” of the rosary. The prayers are all the same, but there are meditations before each decade that are taken from the Maronite liturgical tradition).
As to the rest of Eastern and Oriental Christianity, I’m still searching to learn more.