In the 2002 edition of the Lectionary for Mass, number 28 is “For the Promotion of Charity, or To Foster Harmony, or For Family and Friends.” Surprisingly, there are no readings suggested from the Old Testament. Number 29 is designated “For the Family,” and the Scriptures used for the Holy Family observance after Christmas would be logical possibilities, if a passage from the Hebrew Bible were needed: selected verses from Sirach 3, Genesis 15:1-6, Genesis 21:1-3 (those two are proclaimed together in cycle B, believe it or not) or 1 Samuel 1:20-22, 24-28 (cycle C).
New Testament choices for this Mass include three selections from the Rite of Marriage: Romans 12:3-13 (on gifts), 1 Corinthians 12:31—13:13 (on love), or 1 John 3:14-18 (love and charity triumph over hate).
The Gospel picks are two: community correction (“brother”) in Matthew 18:15-20 and a more inspiring passage from the Last Supper narrative, John 15:12-17.
I would have gone with one of the Holy Family Psalms–128 or 105:1-2, 3-4, 5-6, 8-9 or 84:2-3, 5-6, 9-10. But the Roman Missal suggests two others: the kiss of justice and peace in Psalm 85:7-8, 9, 11-12 or the flock God shepherds in Psalm 100:2, 3, 4, 5
The Mass propers are just two. Psalm 122 for entrance with the antiphon from verses 6 & 8:
For the peace of Jerusalem pray, and may they prosper, those who love you. For the sake of my family and friends, I will say: Peace be upon you.
And the other …
Communion Antiphon Mt 12: 50
Whoever does the will of my heavenly Father is my brother, and sister, and mother, says the Lord.
I suppose any unused of the Psalms from the Liturgy of the Word would be a decent enough choice. As would the wisdom passage from Sirach 3:1-16. Maybe the Beatitudes, too, if something from the New Testament were to be a consideration.
Some years ago, we blogged on Masses And Prayers For Various Needs And Occasions. In the GIRM, sections 368-378 cover the universal regulations on their use. You can check our brief comments here and here and here. The USCCB’s unannotated text on the matter is here.