If only one prospector is chosen during a round, does the other one get a coin placed on it?
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.
From the rules, pg7 under "A new round ..."
Now, the governor takes three doubloons from the bank, placing one each on the three role cards that were not selected during the round.
Although "prospector" seems like one role, there are two people playing it. Call them prospector 1 and prospector 2.
If prospector 1 is chosen for the current round and prospector 2 isn't, prospector 2 will get a coin placed on him. Meaning that he will be chosen the next time someone needs a prospector.
The prospectors were inserted in the game as a "mechanic" to keep the number of agents greater than the number of players by three. There are no prospectors in a three person game, one in a four person game, and two in a five person game.