Deaconesses were an order in the primitive Christian Church. Information is sparse as to their activities at the time, though it is clear they were mostly involved with ministering to other women and girls.
It being improper for males to be physically handling women, deaconesses were commissioned to assist especially in baptism and chrismation.
It is an anachronism to say deaconesses did not perform the same liturgical role as deacons in the early church. That is imputing back in time to deacons a role which they were given considerably later in Church history.
In the early church it is highly likely that deaconesses performed the same liturgical role as deacons, and quite likely more, because of the taboo on (male) priests touching female neophytes, or touching females requiring the sacrament of holy oil for the sick.
It is likely that the actual application of the holy oil onto the body of the women being chrismated was done by the deaconess, and not the priest. The priest did the praying and supervised, but did not touch. Deacons would not have performed this role. As there was no taboo on the priest physically applying the oil to male candidates, there was no need for deacons to be involved in this.
The Japanese Orthodox Church from its inception in the later half of the nineteenth century had some deaconesses. Japan's first bishop Saint Nicholas Kasatkin had a number of deaconesses during his tenure.
At the same time the Russian Orthodox Church, Japan's mother Church, had deaconesses. It seems from the scant material available that the Russian Church has always had deaconesses.
The Greek Orthodox Church has had deaconesses intermittently over the recent centuries, and appears to have usually had deaconesses in its female monasteries from time immemorial.
The Russian Orthodox Church still has deaconesses. 
In female monasteries the role of a deaconess seems necessary for the good order and function of the monastery church. It is more seemly than having male deacons involved there.
The question of having deaconesses perform the liturgical role of deacons in parish churches or cathedrals is a different matter and should be the subject of separate discussion.