Is there any reason one couldn't have a Tiny Sized Druid animal companion? All of the listed one start off as Small or Medium. It just seemed odd that there aren't any tiny ones
You could start with a small-sized Animal Companion, forgo its advancement to medium in favor of +2 to Dex and Con, and shrink it down to tiny-sized with Reduce Person.
Only a few options that I'm aware of for this, though. Sylvan Sorcerer would be the easiest.