Since copper is more reactive than silver, it will displace silver from its solution and form copper nitrate which will go in solution. In doing this the vessel of copper get dissolved to make copper nitrate. Hence we can not store silver nitrate in copper vessel. The reaction is as follows :
Cu + AgNo3 →CuNo3+ Ag
But storing copper nitrate in silver vessel is possible as silver is less reactive than copper so it does not reacts with copper nitrate solution.