Along with the Trinity Hymnal (Copyright © 1990, Great Commission Publications, Inc.) these are some other resources that we use regularly in the singing at New Covenant:
Indelible Grace Hymnbook grew out of the ministry of Reformed University Fellowship (RUF). They have taken many great texts of old hymns and put them to newer melodies.
Sovereign Grace Music is the ministry of Bob Kauflin, and began writing songs for churches over 30 years ago that are biblically and theologically rich.
Getty Music is the ministry of Keith and Kristyn Getty who have written some of the best newer hymnody songs of the present age including "In Christ Alone."
Songs for the Savior is a small songbook New Covenant has put together, composed of many of the newer hymnody and psalms from the links above that we regularly sing in worship. Feel free to download a copy and use it at your own family worship or at your church.
Hymnary.org is an online hymn and worship music database for worship leaders, hymnologists, and amateur hymn lovers alike where you can search or browse hymns by title, tune, meter, key, scripture reference, and more.