Hi again!
I tried a few examples and unfortuneatly, there's nothing with either png size or encoding.
First - we can't notice shaking on Diaco's example because this Santa alredy has all edges moving. I tried to chop off a part of it and then you can see this shaking very clear.
Second - this shaking is not happening if result of frame width multiplied with resize ratio is round number. So - if frame width is 150px and you scale it by 0.5, it's ok, but if you try 0.51, it shakes. Check it all here: http://codepen.io/anon/pen/azWgRO
So at this moment a have no idea how to solve it with the sprites we have.