  While all of the polymorphs of pure NH$_4$I and KI are non-polar, we identify
that (NH$_4$)$_{0.95}$K$_{0.05}$I is ferroelectric and
(NH$_4$)$_{0.87}$K$_{0.13}$I and (NH$_4$)$_{0.83}$K$_{0.17}$I are pyroelectric
through measurements of their pyroelectric current and complex dielectric
constant. The order to disorder phase transitions occur near 245 K. Magnetic
susceptibility measurements indicate that the proton orbitals of the NH$_4$$^+$
continue to become ordered in the ground state in the (NH$_4$)$_{1-x}$K$_x$I
system up to x <= 0.17. The polar phases are proposed to stem from K$^+$ ions
disrupting the symmetry of proton-orbital-lattice interactions between the
NH$_4$$^+$ and I$^-$ ions. Our work introduces a new pathway for the ordered
phases of ammonium-based compounds to potentially become ferroelectric.
