Bob Johnson from: http://tabernacle-of-david.com/catechism.html states:
The majority of the Psalms were originally sung as prophetic songs in David's Tabernacle. They account in detail the expressions of worship offered by the Israelites before the Ark of the Covenant. In addition, they describe the full range of human emotions revealed in the presence of God, from deepest despair to highest joy. The righteous kings of Israel that followed David reestablished Davidic worship within the context of Temple worship. These revivals of Davidic worship paved the way for spiritual renewal and military victory. These times of revival and victory were under Solomon (2 Chr. 5-7) - 101 B.C., Jehoshaphat (2 Chr. 20) - 896 B.C., Joash (2 Chr. 23-24) - 835 B.c., Hezekiah (2 Chr. 29-30) - 726 B.C., Josiah (2 Chr. 35) - 623 B.C., Ezra (Ezra 3:10-13) - 536 B.C. and Nehemiah (Neh. 12:28-47) - 446 B.C.
Bob also notes: Even after David’s time, Davidic worship re-appeared in every subsequent revival mentioned in the Old Testament:
a. Abijah – 2 Chronicles 13:14-15
b. Asa – 2 Chronicles 15:12-15
c. Jehoshaphat – 2 Chronicles 20:18-22
d. Joash – 2 Chronicles 23:12-15
e. Hezekiah – 2 Chronicles 29:25-30
f. Josiah – 2 Chronicles 35:25
g. Zerubbabel – Ezra 2:65, Ezra 3: 10-13
h. Nehemiah – 12: 27, 36, 45-46