I recently came across a few 19th century uses of the term “Modern Orthodoxy Jews/Judaism.” The term was not necessarily used in the same way that we use it today and a fuller discussion must related to the use of the term in a Christian context, but I thought that they were interesting none the less. For some discussion of the origins of the term, see this post by Alan Brill.
Maybe the earliest use by a Jew that I could find was by Claude G. Montefiore. The following is from an article in the Contemporary Review, vol. 42, 1882.
This is also an article by Montefiore that was published in the Jewish Quarterly Review IV, 1892.
This pamphlet was published by the Reform rabbi Gotthard Deutsch in 1898. It is a reprint of an earlier article from the Reform Advocate.
Deutsch also used the term “Modern Orthodoxy” in the Jewish Encyclopedia [hereand here].
This Christian polemical tract against Jews that was published in 1890 even got into the act.
The earliest use that I could find, although I did not do an exhaustive search and I limited myself to English (maybe in German there was an equivalent that was used earlier), was from an article about the 17th century Hugenot pastor Isaac Jacquelot that was published in 1874. The article was a translation of an article in German that was written by Rev. A. Fürat and it was published in the following missionizing journal.
Here is the quote:
Lastly, there is a cookbook that was published in 1897-The Economical Jewish Cook:
A Modern Orthodox Recipe Book for Young Housekeepers.