Ok you guys, I finished off this project about an hour ago.  It got kind of fiddly toward the end & I know that it could have been done a lot better, but I guess that means I learned something, right?  Hopefully the next project will turn out better.
Here I've laid out and pinned a corona for the sun:

I've left one part off so that I can use that area for stuffing.  I sewed around all the other bits, then stuffed it, then sewed up the hole.  Pretty simple.
The next pic is the kind of stitching I used around the outside.  Went down, across and back up.  Didn't loop back, just kept going.  Then when I got to the end I turned around and came back using the same holes to make it stronger & so that it looked the same as the stitching around the face elements (this is from when I was half done)

And here's the finished product:

One insanely happy sun!
Not sure if I am going to keep this for myself  due to it being my first project, or give it to my dad for father's day next weekend.  I mean, I am pretty sure that I am going to keep it, because I am not sure my dad would appreciate a sun pillow with a big shit-eating grin on it.  I wonder if I could think of something else simple to make in time for next sunday.