I came across a question and an answer on the website, http://www.suscopts.org/q&a/index.php?catid=310, that proves King David not the author of all the psalms. If this is so, why do we generalize saying "from the psalms of our father David the prophet and the king..."?
As is mentioned in the third paragraph of the response on the web, nearly one half of the psalms are attributed to King David. Therefore, the vast majority of the psalms prayed in the Agpeya are by him. In 2 Samuel 23:1, David, the Prophet and King, is described as "The anointed of the God of Jacob, and the sweet psalmist of Israel." Other contributors to the Holy Book of Psalms are also remarkable individuals. However, it is David the Prophet, who most exemplifies his profound worship, hope, love, humility, and repentance through his poetry, praise, and melodies. Thus, we borrow those words as though they are ours when we worship the Lord in the same spirit as did David, the Prophet and King.