  CeCo(In$_{0.990}$Hg$_{0.010}$)$_{5}$ is a charge doped variant of the
$d$-wave CoCoIn$_{5}$ superconductor with coexistent antiferromagnetic and
superconducting transitions occurring at T$_{N}$= 3.4 K and T$_{c}$=1.4 K,
respectively. We use neutron diffraction and spectroscopy to show that the
magnetic resonant fluctuations present in the parent superconducting phase are
replaced by collinear $c$-axis magnetic order with three-dimensional Ising
critical fluctuations. No low energy transverse spin fluctuations are
observable in this doping-induced antiferromagnetic phase and the dynamic
resonant spectral weight predominately shifts to the elastic channel. Static
($\tau$ $>$ 0.2 ns) collinear Ising order is proximate to superconductivity in
CeCoIn$_{5}$ and is stabilized through hole doping with Hg.
