SrCo2As2 is a peculiar itinerant magnetic system that does not order magnetically, but inelastic neutron-scattering experiments observe the same stripe-type antiferromagnetic (AF) fluctuations found in many of the Fe-based superconductors along with evidence of magnetic frustration. Here we present results from neutron diffraction measurements on single crystals of Sr(Co1−xNix)2As2 that show the development of long-range AF order with Ni doping. However, the AF order is not stripe type. Rather, the magnetic structure consists of ferromagnetically aligned (FM) layers (with moments laying in the layer) that are AF arranged along c with an incommensurate propagation vector of (0 0 τ), i.e., a helix. Using high-energy x-ray diffraction, we find no evidence for a temperature-induced structural phase transition that would indicate a collinear AF order. This finding supports a picture of competing FM and AF interactions within the square transition-metal layers due to flat-band magnetic instabilities. However, the composition dependence of the propagation vector suggests that far more subtle Fermi surface and orbital effects control the interlayer magnetic correlations.