We report the results of a muon-spin relaxation (mu SR) investigation of La2-xSrxCoO4, 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 <= x less than or similar to 0.6) suggests that the putative stripe ordered phase extends to lower x than previously thought. Further charge doping (0.67 <= x <= 0.9) prevents magnetic ordering for T greater than or similar to 1.5K.