All I can find regarding the Marian Psalter is attributing the term to the Rosary.
As a complete aside, I just found out that you get indulgences by praying the Rosary, which I never knew:
"A partial indulgence is gained, under the usual conditions, when praying a third of the Rosary (5 decades) continuously (i.e., one can't say a decade, go wash the dishes, and return to say the other decades).
A plenary indulgence is gained, under the usual conditions, when it is prayed by a family group or publicly in a church or oratory. The decades' Mysteries must be announced, and the Mysteries meditated on."
Learn something new every day!