  In 2+1 dimensional nonrelativistic Chern-Simons gauge theories on $S^2$ which
has a global $SU(M)$ symmetry, the semilocal Popov vortex equations are
obtained as Bogomolny equations by minimizing the energy in the presence of a
uniform external magnetic field. We study the equations with many flavors and
find several families of exact solutions. The equations are transformed to the
semilocal Liouville equations for which some exact solutions are known. In this
paper, we find new exact solutions of the semilocal Liouville equations. Using
these solutions, we construct solutions to the semilocal Popov equations. The
solutions are expressed in terms of one or more arbitrary rational functions on
$S^2$. Some simple solutions reduce to $CP^{M-1}$ lump configurations.
