Sinking adverbs are provided in this article. The words listed here are commonly found along with the verb sinking in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb SINKING.
actually, apparently, constantly
continually, deeply, evidently
finally, gently, gradually
heavily, nearly, quickly
rapidly, really, slowly
steadily, suddenly
Hope this word list had the sinking adverb you were looking for. In addition to adverbs used with sinking, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.