The best replacement for reindeer is caribou.

The best alternatives to reindeer are rated as following:
★★★★★  caribou
★★★★  deer
★★★  moose
★★  elk
★★  reindeers
★  venison
★  regular deer
  stag
  antelope
  elves
  whitetail deer
  reindeer
  mule deer

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

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



Google Trends

Scale is based on the average worldwide traffic of reindeer in all years. Click on graph for more.
reindeer
caribou
deer