There have been a number of books published in Klingon. As far as I know, all but one have had some kind of agreement with Paramount, or have been published through Simon and Schuster (a division of Paramount).
There have been many stories, songs, poems, etc that have been “published” online. As far as I know, none have had any kind of agreement with Paramount.
The KLI has published tlhIngan Hol books in the past, and may be able to publish yours, but there are a number of caveats to taking that path.
Note that I am not a lawyer. You may want to contact one (or work with your publisher to contact one) for a more definitive answer.