Premium drops are random, determined by a formula that takes into account friendship, mood, and daily luck (for ducks and rabbits). There's no clear cutoff value. More is better, of course.
I just assumed it was petting them. But yeah, walk up to them and press a button and look for a heart. Do it every day. If there's a grey storm cloud thing instead of a heart then they are grumpy, make sure you didn't lock them outside overnight, make sure they have a heater (especially if it's winter), make sure they have food.