The recycling of critical metals like cobalt and nickel from spent lithium-ion batteries (LIBs) is of immense importance in sustainable manufacturing. This work aims to purify Co(II) and Ni(II) present in acidic and ammonia solutions using ion exchange. AG-1-X8 resin modified with thiocyanate anions (R4N+SCN− resin) was used to separate a small amount of Co(II) from HCl and H2SO4 solutions containing Ni(II) and Si(IV) at pH 3, and the effect of factors such as pulp density, shaking time, and Ni(II) concentration on the adsorption of Co(II) was investigated. The difference in the adsorption behaviour of metal ions onto the R4N+SCN− resin from HCl and H2SO4 solutions was insignificant. Increasing the Ni(II) concentration in the feed negatively affected the loading efficiency of Co(II). The complete elution of the metals from the loaded resin was attained with a 5% NH3 solution. Purolite C100 resin was selected for the purification of Co(II) from a 10% (v/v) NH3 solution containing a small amount of Ni(II), and the best conditions for the complete adsorption of both Co(II) and Ni(II) were determined. Selective elution of Ni(II) over Co(II) from the loaded resin was achieved by dilute H2SO4 solution. The purity of Co(II) in the solution after elution with 2.0 mol/L H2SO4 from the Ni(II) free resin was higher than 99.99%. Ion exchange was effective for purifying a weak acidic or ammonia solution in which there is a significant difference in the Co(II) and Ni(II) concentrations.