The best replacement for continuous lighting is flash.

The best alternatives to continuous lighting are rated as following:
★★★★★  flash
★★★  strobe lighting
★★★  strobe
★★  strobes
★★  flash lighting
★  studio flash
  flash photography
  flash studio

Your alternative for continuous lighting is not listed? Suggest!
Speaking about continuous lighting, one probably shouldn't forget about softbox.

Other search terms related to continuous lighting and their ratings are:
★★★★★ softbox
★★★★ softboxes
★★★ soft box
You have in mind a companion for continuous lighting and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of continuous lighting in all years. Click on graph for more.
continuous lighting
flash
strobe lighting