How long can you store the bones of a chicken in the refrigerator?
Rumtscho gives the answer in the comments:


  No more than 4 hours spent between 5°C and 60°C, cumulative since
  purchase (assuming the butcher followed correct procedures). It is
  very restrictive, but most people think it is sensible to follow it
  (and American restaurants are legally obliged to)


And about freezing which I will use:


  if you want to stockpile bones, freeze them. They will keep for months
  that way. This question was about a refrigerator.