The best replacement for cheers is salute.

The best alternatives to cheers are rated as following:
★★★★★  salute
★★★★★  seinfeld
★★★★  frasier
★★★★  chants
★★★★  toast
★★★  yells
★★★  thanks
★★★  regards
★★  chears
★★  here's
★  cheerio
★  cheer
★  best regards
★  toasts
★  sincerely
★  salud
  gilligans island
  bye
  thank you
  prost
  heres

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

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



Google Trends

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cheers
salute
seinfeld