CaCo2−yAs2 is a unique itinerant system having strong magnetic frustration. Here we report the effect of electron doping on the physical properties resulting from Ni substitutions for Co. The single crystals of Ca(Co1−xNix)2−yAs2 were characterized by single-crystal x-ray diffraction, energy-dispersive x-ray spectroscopy, magnetization M versus temperature T , magnetic field H, and time t, and heat capacity Cp(H, T ) measurements. The A-type antiferromagnetic (AFM) transition temperature TN = 52 K for x = 0 decreases to 22 K with only 3% Ni substitution and is completely suppressed for x > 0.11. For 0.11 ≤ x ≤ 0.52 strong ferromagnetic (FM) fluctuations develop as revealed by magnetic susceptibility χ(T ) = M (T )/H measurements. For x = 0.11 and 0.16, competing AFM and FM interactions result in spin-glass behavior at low T as evidenced by observations of thermomagnetic hysteresis and magnetic relaxation. Enhanced FM fluctuations are also found for the x = 0.21 and 0.31 crystals, where χc increases significantly at low T . A large χ anisotropy in these compositions where χc is up to a factor of two larger than χ ab suggests that the FM spin fluctuations are quasi-1D in nature. Weak FM contributions to M (H = 0) were found at T = 2 K for x = 0.11-0.31. Heat-capacity Cp(T ) measurements revealed the presence of FM quantum spin fluctuations for 0.11 ≤ x ≤ 0.52, where a logarithmic T dependence of Cp(T )/T is observed at low T . The suppression of AFM order by the development of strong FM fluctuations in Ca(Co1−xNix)2−yAs2 crystals suggests the presence of a FM quantum-critical point at x ≈ 0.20. Our density-functional theory (DFT) calculations confirm that FM fluctuations are enhanced by Ni substitutions for Co in CaCo2−yAs2. The Sommerfeld electronic heat-capacity coefficient is enhanced for x = 0, 0.21, and 0.42 by about a factor of two compared to DFT calculations of the bare density of states (DOS) at the Fermi energy, suggesting an enhancement of the DOS from electron-phonon and/or electron-electron interactions. The crystals with x > 0.52 do not exhibit FM spin fluctuations or magnetic order at T ≥ 1.8 K, which was found from the DFT calculations to result from a Stoner transition. Superconductivity is not observed above 1.8 K for any of the compositions. Neutron-diffraction studies of crystals with x = 0.11 and 0.16 in the crossover regime 0.1 x 0.2 found no evidence of A-type ordering above 4.8 K within experimental resolution as observed in the parent compound with x = 0. Furthermore, no other common magnetic structures, such as FM, helical stacking of in-plane FM layers, or in-plane AFM structure, were found above 4.8 K with an ordered moment greater than the uncertainty of 0.05 µB per transition-metal atom.