Relied adverbs are provided in this article. The words listed here are commonly found along with the verb relied in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb RELIED.
absolutely, actually, apparently, chiefly, commonly, completely, confidently, constantly
entirely, especially, exclusively, extensively, firmly, formerly, frequently, fully
generally, greatly, heavily, historically, implicitly, increasingly, initially, justifiably
largely, mainly, mostly, necessarily, previously, primarily, principally, probably
reasonably, safely, simply, solely, strongly, thoroughly, traditionally, typically
ultimately, usually, wholly
Hope this word list had the relied adverb you were looking for. In addition to adverbs used with relied, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.