There are rainbow lorikeets that live in the parks around here 
they are so colourful. They have verdant green wings like leaves, an orange belly like ripe summer fruit, and a head as blue as the sky. So they would totally blend in when they land on our persimmon trees.
I like to see them free, but also secretly want them as a companion sometimes
Other than that, mystical creatures that would be cool as companions are phoenixes 
, dragons 
and unicorns 