"Beneath the Cross of Jesus" (no, not the traditional hymn) by Keith & Kristyn Getty and "The Power of the Cross" by Keith Getty and Stuart Townend. Keith is gaining a name for writing new hymns for the church and these 2 can easily be done as solos or congregational music.
ok, this may be a late response...but HEY! I just joined tonight! lol!
Here's an oldie but goodie, ..... although there are quite a few great songs found on "The Cross" From the "Why we worship" series of Vineyard.... my personal fave that always moves me is the song "Tears"- by Sheri Keller
would be an AWESOME remake!