In this paper, we study equilateral spherical drawings of planar Cayley graphs. We focus on the case when the underlying group is generated by two rotations. In this case, the set of equilateral drawings can be parameterized by spherical ellipses on the unit sphere. Besides, we give an explicit formula to describe the shortest equilateral spherical drawing and the longest spherical equilateral drawing. Furthermore, we studied the drawing of Schreier coset graphs arising from these equilateral drawings.