When looking through recipes in older cocktail books, you will sometimes come across recipes (although very few) which list celery bitters as an ingredient. It is unclear when celery bitters disappeared from the scene, but it is expected that it was sometime during American Prohibition, if not before.
Fortunately, some artisinal bitters companies have started making their own version of this once defunct product, perhaps the best known one comes from The Bitter Truth, in Germany.