Check out the Scottish Psalter, whose rendering of Psalm 23 many of us know by heart: http://www.cgmusic.org/workshop/scot1635_frame.htm. Many of these poeticized versions of the Psalms you can sing to familiar hymn-tunes if only you become familiar with some of the common meter schemes:
Common meter (8-6-8-6) – for example: Amazing Grace.
Short meter (6-6-8-6) – for example: Rise up, O men of God
Long meter (8-8-8-8) – for example: Praise God from whom all blessings flow
For an extended explanation, see the Wikipedia article “Meter (hymn”: https://en.wikipedia.org/wiki/Meter_(hymn)
I am trying to set Scriptures to acappella songs. Go here for examples: https://www.youtube.com/user/stchsingleton (over half a million views).