A quick internet search turns up the well-known text of the Divine Praises, along with a note attributing its origins to Fr Luigi (Louis? or Aloysius?) Felici, S.J. in 1797, as a form of reparation for blasphemy. (I found a copy on Google Books of the oration preached at his funeral, which indicates he died in 1818; and another search turned up the fact that he was born in 1736.) It was written in Italian, and the Latin is a later translation (as is the form in English, of course). The original form had but eight lines, to which successive additions have been made. Pius VII granted an indulgence for its recitation on 23 July 1801; I haven't found a copy of Felici's original, so I do not know if Pius VII changed or enlarged it, as some sources seem to suggest.
Succeeding Popes have added ever more indulgences and blessings to it (though those indulgences have since been watered down); but it turned out to be quite hard to discover exactly when. Recourse had to be had to the Acta Apostolicæ Sedis, and other sources, to find the official decrees adding each blessing, and I have found a puzzling reference to the date when Bl Pius IX made the first addition in honour of the Immaculate Conception, suggesting that it was added, not in the year 1856 as other sources claim, but on 27 April 1851, some years prior to the dogmatic definition of 1854. Herewith, the Divine Praises, with the dates of each addition noted:
Blessed be God.
Blessed be his Holy Name.
Blessed be Jesus Christ, true God and true man.
Blessed be the name of Jesus.
Blessed be his Most Sacred Heart. (Leo XIII, 2 February 1897)
Blessed be his Most Precious Blood. (St John XXIII, 12 October 1960)
Blessed be Jesus in the Most Holy Sacrament of the Altar.
Blessed be the Holy Spirit the Paraclete. (Bl Paul VI, 27 April 1964)
Blessed be the great Mother of God, Mary Most Holy.
Blessed be her holy and Immaculate Conception. (Bl Pius IX, 25 April 1851)
Blessed be her glorious Assumption. (Pius XII, 23 December 1952, 8 April 1953)
Blessed be the name of Mary, Virgin and Mother.
Blessed be St Joseph, her most chaste spouse. (Benedict XV, 23 February 1921)
Blessed be God in his Angels and in his Saints.
There are two dates given for the insertion of blessing of the Assumption, since by an embarrassing error it was first commanded to be illogically inserted before that of the Immaculate Conception, so a correction had to be published a few months later.
I recall reading somewhere, in a book on the Eucharist by Louis Bouyer I think, that two desirable additions to these praises would be "Blessed be the holy Apostles" (those pillars of the Church founded by their Master) and "Blessed be the holy Catholic Church" - the latter, being the Bride of Christ, oft reviled by the world's attacks (all too often deservedly attracted, sad to say, by the outrageous crimes of her sinful members), yet remaining holy and spotless in her essential nature despite every attempted besmirching: she is, after all, casta meretrix.