  We report the results of a muon-spin relaxation ($\mu$SR) investigation of
La$_{2-x}$Sr$_{x}$CoO$_{4}$, an antiferromagnetic insulating series which has
been shown to support charge ordered and magnetic stripe phases and an
hourglass magnetic excitation spectrum. We present a revised magnetic phase
diagram, which shows that the suppression of the magnetic ordering temperature
is highly sensitive to small concentrations of holes. Distinct behavior within
an intermediate $x$ range ($0.2 \leq x \lesssim 0.6$) suggests that the
putative stripe ordered phase extends to lower $x$ than previously thought.
Further charge doping ($0.67 \leq x \leq 0.9$) prevents magnetic ordering for
$T \gtrsim 1.5~{\rm K}$
