Customary - stand, but both are acceptable. I assume that you are specifically referring to praying the Hours by yourself or in a small group? The Hours developed out of monastic practice so they were not traditionally prayed in the manner of the Roman Rite, alone with a book. In parish setting, the Hours would be celebrated on the eve of great feasts and Sundays and then also before Divine Liturgy. But it is certainly not uncommon, for some to pray at least some of the Hours of the Byzantine Rite at home, either in full or with abbreviations. Typically First Hour and small compline for example.
There are a few books that have adapted the hours to be prayed by clergy and laity alone or in small groups. The traditional posture is to stand even in these case or during your private prayer rule but this is not a hard and fast rule.