You guys have to think a bit outside the box to get this done. Don't try to unwrap a sphere, but unwrap a planar mesh and warp that into a sphere, preserving it's UVs. Here's how to do it in Blender. Some general understanding of Blender basics is required though. Hope that helps!
Make sure your cursor is centered (shift+c)
Add->Mesh->Grid (Choose whatever res you like, for such a huge mesh like a skydome you can keep default or even res up!!!)
Move the grid up the z-axis for one unit, either in the transform properties (N-key) or manually g,z,1
Next go into edit mode, select all verts and unwrap with default unwrap method, should provide you some simple square UVs.
From
front view!!! Press shift+w,180 (tansform->warp). You’ll end up with an open cylinder. Switch into
side view!!! and press shift+w, 360, this will warp the cylinder into a sphere, but your UVs will still remain square.
At last, remove double verts and apply some texture to your sphere, center pivot point, done!!!