In Puerto Rico If only one prospector is chosen during a round, does the other one get a coin placed on it?
Yes.

Any role not chosen at the end of the round gets a coin placed on it.

I can't find the official rules online, but I can point you to the Universal Head rules summary, which says, under "Reset the Roles":


  Place one doubloon on each of the three role cards not
  chosen this round and then return all role cards.