The structures, magnetism, and electronic transport properties of (La1+xSr1-x)CoRuO6 (-0.50 less than or equal to x less than or equal to 0.25) double perovskites have been investigated. All samples are found to crystallize with the monoclinic P2(1)/n superstructure. An increase of antisite disorder with \x\ is found to be controlled by a reduction in the average charge and size difference between the Co and Ru states. Neutron diffraction results for (LaSr)CoRuO6 show the presence of a long-range, ordered antiferromagnetic state with propagation vector (1/2 0 1/2) below 85 K. Hole doping (x < 0) enhances the Neel temperature slightly, whereas electron doping (x > 0) results in a sharp decrease. Resistivity measurements showed all compositions to be variable-range-hopping semiconductors, where hole doping decreases the resistivity by 2 orders of magnitude, but electron doping has a much less pronounced effect.