Unique spatial eigenmodes for the spherical coordinate system are shown to be successfully synthesized by properly allocated combinations of current distributions along θ' and φ' on a spherical conformal array. The allocation ratios are analytically found in a closed form with a matrix that relates the expansion coefficients of the current to its radiated field. The coefficients are obtained by general Fourier expansion of the current and the mode expansion of the field, respectively. The validity of the obtained formulas is numerically confirmed, and important effects of the sphere radius and the degrees of the currents on the radiated fields are numerically explained. The formulas are used to design six current distributions that synthesize six unique eigenmodes. The accuracy of the synthesized fields is quantitatively investigated, and the accuracy is shown to be remarkably improved by more than 27dB with two additional kinds of current distributions.