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We report neutron diffraction results for the body-centered-tetragonal series Eu⁢(Co1−𝑥⁢Ni𝑥)2−𝑦⁢As2, 𝑥=0.10, 0.20, 0.42, and 0.82, 𝑦≤0.10, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with 𝑥, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For 𝑥=0.10 and 0.82 we find 𝑐-axis helix ordering of the Eu magnetic moments (spins) similar to 𝑥=0 and 1, with the spins oriented within the 𝐚𝐛-plane. For 𝑥=0.20 and 0.42 we find higher-temperature 𝑐-axis ferromagnetic (FM) order and lower-temperature 𝑐-axis cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature 𝑐-axis FM phase for intermediate values of 𝑥, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that 𝑐-axis itinerant-FM ordering of the Co/Ni spins could provide a molecular field that drives FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature 𝑐-axis cone order.