The best replacement for cop is firefighter.

The best alternatives to cop are rated as following:
★★★★★  firefighter
★★★  fireman
★★  cop
★★  eer
★★  skater
★  cia
★  soldier
★  gonzaga
★  drop
★  skateboarder
★  lawyer
★  thug
★  vet
★  sheriff
★  paramedic
★  hspf
★  marine
★  teacher
★  bob sapp
  pat barry
  gabriel gonzaga
  wanderlei silva
  cat
  police
  racer rivals
  xom
  cop killer
  drifter
  deer
  mostapha al turk
  bad cop
  nfl safety
  firemen
  dos santos
  cowboy
  cop youtube
  clown
  kw ton
  silva
  mir
  seer
  eddie sanchez
  bike
  robber
  boop
  cvx
  biker
  vietnam vet
  mir video
  cheick kongo
  emt
  fob

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

Other search terms related to cop and their ratings are:
★★★★★ badge
★ out a badge
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Google Trends

Scale is based on the average worldwide traffic of cop in all years. Click on graph for more.
cop
firefighter
fireman