The attached research found the optimum condition for good adhesion was obtained by electroplating two-layered copper deposition. The first, a “thin” layer deposited in alkaline bath of 0.1 mol dm− 3 CuSO4, 0.5 mol dm− 3 citric acid (C6H8O7) at pH = 10. The addition of citric acid formed copper complexion in the alkaline solution, and resulted in improved deposition of copper at wide current density range. The second thick copper layer was deposited with conventional bath, which composition is 0.75 mol dm− 3 CuSO4 and 0.3 mol dm− 3 H2SO4.
If you use a solution of a copper salt such as copper sulphate, yoy will get a layer of copper, which does NOT adhere to the steel and easily peels off. You need to use a solution containing copper in a complex compound, which will not react with steel without application of electric current. The previous reply by Ameer K Ibraheem contains the same fact.
When I was a high school sudent, approx. 70 years ago, I fould a prescription in some handbook and it worked perfectly. Unfortunately I only remember that the electrolyte contained potassium cyanide and was, therefore, extremely poisonous. As Mr. Ibraheem correctly wrote, you can use a conventional solution such as copper sulphate, if you wish to thicken the thin layer obtained in the first explained step.