I've found a lot of info about different hymns and spirituals related in one way or another to the "Hiding Place" quoted by Mrs. Prince in her book.

None of these hymns and song lyrics are the same as the ones that appear at the end of Mrs. Prince's book, but they all seem related to Psalm 32 (v. 7) and/or Psalm 119 (v. 114).

"Thou Art My Hiding-Place"
Words: Psalm 32:7-11 Charles Wesley, c. 1743
Music: "Ernan" Lowell Mason, 1850
Thou Art (Wesley)

Jehoida Brewer: Hail, Sovereign Love (Gospel Magazine, 1776) / Cyberhymnal:
Brewer (Sovereign Love)

In the Harmonia Sacra Handbook, it is refered to as a 'folk hymn' dating from 1810, and it is attributed to Major John Andre: Harmonia / Major Andre (Sovereign Love)

IBC Berlin had a version in their list of songs from Sept. 11 2005: You Are My Hiding Place: Celebration Hymnal # 700: IBC Berlin (Hymn #700)

There's also "The Hiding-Place" in the Early Shakers' Millennial Praises Gospel Hymns from 1813 (see Hymn 3) / : Early Shakers (1813)


Cyberhymnal has an hymn called "Thou Art My Hiding Place, O Lord"
Words: Thomas Raffles, 1838.
Music: "St. Leonard (Hiles)," Henry Hiles, 1867 (MIDI, score) : Thou Art My Hiding Place, O Lord

Isaac Watts (55. THE HIDING-PLACE IS NIGH)
Coprighted by R.E. Hudson in Gospel Jewels for Sabbath Schools (pub : 1885): Hiding Place (Watts)

On their CD "Redemption Songs", Jars of Clay have a version called "Hiding Place" which is attributed to Daniel Herbert (author, 1814). Apparenty, this version is from the Gadsby's Hymns:
Hinding Place (Herbert) Info
Hiding Place (Herbert) Lyrics

The line "The rock cried out « no hiding place»" appears in a spiritual titled « Where Shall I Go ?» (from Negro Spirituals Online): Where Shall I Go?

Both "Where Shall I Go?" and "No Hiding Place" seem related to the song "Heaven Bell a Ring" which appears at #20 in Allen & Ware's book "Slave Songs of the United State" (1867): Allen & Ware (Slave Songs)

Finally, there's the bluegrass song by Bill Monroe : I've Found a Hiding Place

I thought it was ok to post all these infos in this thread (in chronological order). I've checked all links and they're supposed to work. Sometimes you have to go down the page to find the lyrics/infos to "Hiding Place" (aka "Sovereign Love").

The Prince version is still a mystery.