I have an Eevee that likes to fight well... everything. A Charmander, a Chikorita who really likes to hug people and be hugged, a Piplup who's affectionate but also not really that interested in battling, and Pidgey who likes to sit on my shoulder.

I don't really know the Happiny or Diftloom I recently got that well yet though. Maybe those two will stay still a little easier than most of my others.