Jer 31:7-14 (Christmas 2 ABC; Proper 25 B)
Ps 72:1-17, 10,14 (Christmas 2 ABC; Advent 2 A)
Eph 1:3-14 (Christmas 2 ABC; Proper 10 B)
Jn 1:(1-9) 10-18 (Christmas 2 ABC; Advent 3 B; Christmas III ABC)
Four out of seven years has two Sundays between December 25th (Christmas) and January 6th (Epiphany). As such, this Sunday is only celebrated just more than half of the time.
Christmas 2 in all years focuses on John 1. Provisions are made to ensure that there is no overlap with the optional reading from John on Christmas (This is known as Christmas III). However, should John not be used for Christmas, I would recommend utilizing the whole of John 1, because it only occurs on the festivals of Christmas and Christmas 2, and it is a cornerstone for our understanding the incarnation of Christ.
Note that Advent 3 included excerpts from this, focusing on the preaching of John the Baptist on Jesus.