The best replacement for speedlight is strobe.

The best alternatives to speedlight are rated as following:
★★★★★  strobe
★★★★  monolight
★★★  studio strobe
★★  studio light
★★  built in flash
★★  continuous light
★  strobe light
★  softbox
★  ring flash
★  external flash
★  lens
★  alien bees
★  led light
  studio flash
  quadra
  lightscoop

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

Other search terms related to speedlight and their ratings are:
★★★★★ softbox
★★★ beauty dish
You have in mind a companion for speedlight and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of speedlight in all years. Click on graph for more.
speedlight
strobe
monolight