In the early church Good Friday was a day of fasting. In the eastern church it wasn’t necessarily Friday: they followed the Jewish Passover festival which could take place on any day of the week. In the west, especially in Rome, the great festival was celebrated on the Sunday after Passover.)
Whatever the case, in the early church it was a day of fasting. The fourth century Apostolic Constitutions says that the day should be marked by a fast. Certainly the baptismal candidates fasted on the day in preparation for their baptism at dawn on Easter morning. The Apostolic Tradition says:
Those who are to receive baptism shall fast on the Preparation of the Sabbath [i.e. Friday]
Apart from that I’ve not been able to find any specific instructions in the church fathers about commemorating Jesus’ death. Detailed liturgy and the idea of the three day festival (called the Easter Triduum) apparently doesn’t evolve until the fourth century.
So, did the second and third century Christians not commemorate Christ’s death? On the contrary. Reading The Apostolic Tradition indicates that they remembered it every single day. It begins first thing in the morning:
If you are at home, pray at the third hour and praise God. If you are elsewhere at that time, pray in your heart to God. For in this hour Christ was seen nailed to the wood…
Pray also at the sixth hour. Because when Christ was attached to the wood of the cross, the daylight ceased and became darkness…
Pray also at the ninth hour a great prayer with great praise… For in that hour Christ was pierced in his side, pouring out water and blood, and the rest of the time of the day, he gave light until evening…
The Apostolic Tradition was written in the early third century (215 onwards) and probably for a church in Rome. There’s a lot of extra stuff in these bits, links to the Old Testament and some symbolism which I haven’t quite grasped yet. But the interesting thing is that Christians for whom The Apostolic Tradition was written were expected to pray at 9 am, 12 noon and 3 pm, and these prayers were tied in to remembering Christ’s death. The practice grew out of the pattern of Jewish worship based around the temple, and is also reflected in Acts 10, where Peter and Cornelius are depicted as praying at these times.
So the implication, in The Apostolic Tradition at least, is that the early church did commemorate ‘Good Friday’, but they did it every day of their lives.
Each day was a memory of Easter. It was Good Friday, everyday.