I don't have any activities for Psalm 13 but I do believe Ted Sandquist once wrote a song to this Psalm. You might be able to track it down (and others) at
Global Worship Initiatives.
It's been a long time so I don't know if either he considers what he does "post-modern" or "emergent" but you can't help but love his music!
In the early '70's before I knew the Sandquists, I was part of a Christian folk group ((for a very short time and actually met the Lord there though I "grew up" in the church) in upstate NY. At the time that group (Kyiake)'s parent was a Canadian Christian teen folk group called Hakamu. Jeremy Sinnott was one of the group leaders. A couple of years ago I discovered that God has continued to use Jeremy's music internationally as well.
It's just interesting! The music of both worship music song-writers had a significant affect on my walk with God.
If you ever read this, "Blessings you guys!"