Very complex ask. If you break the sphere into slices vertically like and orange using split body tool. But also split the sphere into sections horizontally e.g. like parallels at the lower 135th parallel, equator and upper 45th parallel. Then carefully unfold and flatten the pieces would one way to project to the surface for a regular pattern. Tedious to be sure
If you do not need uniform spots then drawing the spots on a plane and carefully rotating the plane or the sphere and project them onto the sphere maybe.
A search will net you some oldie but goodies