Effect of Ni substitution on the fragile magnetic system La₅Co₂Ge₃

La₅Co₂Ge₃ is an itinerant ferromagnet with a Curie temperature, TC, of ~ 3.8 K and a remarkably small saturated moment of 0.1 μB/Co. Here we present the growth and characterization of single crystals of the La₅(Co₁₋ₓNiₓ)₂Ge₃ series for 0.00 ≤ x ≤ 0.186. We measured powder X-ray diffraction, composition as well as anisotropic temperature dependent resistivity, temperature and field dependent magnetization along with heat capacity on these single crystals. We also measured muon-spin rotation/relaxation (μ SR) for some Ni substitutions (x = 0.027, 0.036, 0.074) to study the evolution of internal field with Ni substitution. Using the measured data we infer a low temperature, transition temperature-composition phase diagram for La₅(Co₁₋ₓNiₓ)₂Ge₃. We find that TC is suppressed for low dopings, x ≤ 0.014; whereas for 0.036 ≤ x ≤ 0.186, the samples are antiferromagnetic with a Neel temperature, TN, that goes through a weak and shallow maximum (TN ~ 3.4 K for x ~ 0.07) and then gradually decreases to 2.4 K by x = 0.186. For intermediate Ni substitutions, 0.016 ≤ x ≤ 0.027, two transition temperatures are inferred with TN > TC. Whereas the $T-x$ phase diagram for La₅(Co₁₋ₓNiₓ)₂Ge₃ and the $T-p$ phase diagram determined for the parent La₅Co₂Ge₃ under hydrostatic pressure are grossly similar, changing from a low doping or low pressure ferromagnetic (FM) ground state to a high doped or pressure antiferromagnetic (AFM) state, perturbation by Ni substitution enabled us to identify an intermediate doping regime where both FM and AFM transitions occur.