What do you mean it isn't a Church-approved devotion? Which Church are you referring to, the Lutheran church? The person that the devotion originated from, Faustina Kowalska, was canonized in 2000, and a plenary indulgence was granted for the Divine Mercy Sunday devotions this past year.
Speaking of the rosary, the current form of joyful, sorrowful, and glorious mysteries for the rosary came from Pope Pius V in 1569, who was a former Dominican. Before that, the rosary was known as a "Paternoster," for obvious reasons.
My calendar doesn't have any "divine mercy" Sunday.
Anyways, here is an excerpt from the Daily Catholic site:
A local devotion under the title of "Divine Mercy" was approved by the Ordinary of Vilnius in 1936 and from there spread rapidly, especially after World War II in the United States. It appears that Sr. Faustina could not write, save a few lines phonetically. Most of her "diary" was concocted by her sisters after her death. Because of the incongruities of the dairy (different handwriting, different use of terms), the devotion was suppressed, and the book of her diary was placed on the Index Librorum Prohibitorum [Index of Forbidden Books]. This decision was upheld by Pope John XXIII in 1958/59. In early 1978, a Polish cardinal petitioned the Vatican to remove the suppression of the devotion, which was being practiced without sanction in his diocese, and the Vatican replied in the negative, confirming the suppression.