I can tell you what my diamond dove liked, but he was weird. He liked to swing, plastic toys with beads he could push back and forth, pinatas (although he couldn't shred it, he did like to peck at it), and bells. He liked to make noise, but he was small, so toys were limited. He liked to play with the shredded bits from Bella's toys.
His favorite activity was foraging in on the floor when it was covered with bits of millet and lots of shredded papers. That's a natural behavior for them, so that's why he liked it.