/me electronic pet Birkal
I looked into the Cherrim thing, and indeed finding an animated sprite of Sunshine Forme Cherrim is tough.
I took my Sunny Day Cherrim in Pearl into battle, and I found that in D/P, Sunshine Cherrim does not
have a separate sprite from regular Cherrim.
But then I wondered where Bulbapedia got their non-animated icon of Sunshine Cherrim from. So off to Black. I caught a Cherrim, taught it Sunny Day, and brought it into battle. In B/W, Sunshine Cherrim does
have a different icon from regular Cherrim. It isn't terribly well animated - as far as my eye can tell it's the same image moving up and down one pixel each frame.
BUT it's not the same as the Bulbapedia icon (and no, I have no idea where they got that). Luckily, veekun had the first frame of the actual Sunshine Cherrim, and as I said, the art doesn't change from frame to frame. So I tried my hand at animating the thing myself with GIMP. I appreciate you having animated Volcarona since I was able to use that image as reference while figuring out the positioning and timing of the Cherrim icon within the 32 x 32 grid.
veekun's first frame:
my shot at animating the thing:
EDIT: The list of alternate formes does not have the 26 Unowns, but fortunately Bulbapedia has the animated pngs for them, which you can find in this gallery