Can you store copper sulphate solution in a zinc pot?

No, zinc pot cannot store copper sulphate solution because the standard electrode potential (E° ) value of zinc is less than that of copper. So, zinc is stronger reducing agent than copper.

${{Zn}^{2+}}$(aq) + 2${{e}^{-}}$ --------» Zn (s) E° = -0.76 V
${{Cu}^{2+}}$(aq) + 2${{e}^{-}}$ --------> Cu(s) E° = - 0.34 V

So, zinc will lose electrons to Cu2+ ions and redox reaction will occur as follows:

Zn (s) + ${{Cu}^{2+}}$(aq) ---------> ${{Zn}^{2+}}$(aq) + Cu(s)