From continent +‎ -ly.

continently (comparative more continently, superlative most continently)

1. In a continent, chaste, moderate manner

   Synonyms: chastely, moderately, temperately; see also Thesaurus:virtuously

   • 1861-1862, Henry Parkes, Australian views of England:

     All this time your humble correspondent was continently waiting in the grand corridor leading from the Commons to the Lords, which, however, is by far the best place for the curious spectator at this stage of the proceedings.

   • 1917, Mary MacLane, I, Mary MacLane:

     I swear at my life's perversities with only a fatigued contempt due partly to bodily fragileness but mostly to a cold continently reckless mood which is clasped on me like a strong stupefied devil-fish.

2. continuously

   Synonyms: constantly, persistently, unremittingly; see also Thesaurus:continuously

   • 1895–1897, H[erbert] G[eorge] Wells, The War of the Worlds, London: William Heinemann, published 1898, →OCLC, (please specify the page number(s)):

     A violent explosion shook the air, and a spout of water, steam, mud, and shattered metal shot far up into the sky. As the camera of the Heat-Ray hit the water, the latter had continently flashed into steam. In another moment a huge wave, like a muddy tidal bore, but almost scaldingly hot, came sweeping round the bend up-stream.

• “continently”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.