As I understand from your question, we should synthesize nickel sulfate first from nickel (II) oxide and sulfuric acid and second from nickel carbonate and sulfuric acid.
The chemical reactions will look like this:
NiO (s) + H₂SO₄ (aq) → NiSO₄ (aq) + H₂O (l)
NiCO₃ (aq)* + H₂SO₄ → NiSO₄ (aq) + H₂CO₃ (aq)
but carbonic acid will decompose to carbon dioxide and water
H₂CO₃ (aq) → CO₂ (g) + H₂O (l)
(*) NiCO₃ has a poor solubility in water, but enough to start the reaction.
