I just realized that I coined the adverb "sonnetarily" in one of my sonnets a few months ago, from my Secret Sonnet #3 - here's how it begins:
I possess not what is necessary
To win your love. In a world much better
I could seduce you sonnetarily,
With iambus, syllable and letter.
The only word that is similar if you do a Google search is the adverb monetarily.
How do we know these are adverbs? I'll let the Electric Company and Tom Lehrer explain on Youtube.
