On March 8, 2009, His Eminence Archbishop Hovnan Derderian paid a pastoral visit to the Armenian Church of Ventura County, based in the City of Thousand Oaks. Upon the conclusion of the liturgy, the Primate performed the first baptism to be held at the newly established parish.
What about the celebration of Holy Baptism DURING Divine Liturgy? As far as I knew in the Armenian Church the same priest could not celebrate the same day the Divine Liturgy and the sacraments of Christian Initiation. Apparently this rubric is no more observed.
According to the ancient Typikon of Hagia Sophia the celebration of Baptism took place during the Old Testament readings of Holy And Great Saturday Vesperal Liturgy or before the celebration of the Divine Liturgy (Theophany, Pentecost, Lazarus Saturday). In the Roman Eastern Vigil (in its cassical form) the celebration of Baptism took also place after Old Testament readinds (after New Testament readings in Paul VI Roman Missal). The celebration of Baptism during Great Saturday Vesperal Liturgy or at the begining of the Divine Liturgy (before Small Entrance) is not unknown between Orthodox and Byzantine Rite Catholics.
What about our Oriental Orthodox brothers and sisters?