Silver Mines appear when you use your machete to expand the borders of your town. They always appear with small Silver Pebbles around them. If you find some Silver Pebbles at the border of your town, then you should explore nearby to find the Silver Mine.
Silver Mines take one hour to be harvested to get 163 Silver Coins and 15 XP. After mining, it takes another hour before you can mine again, so each mine can only be harvested every two hours. This will provide you with a steady supply of Silver Coins.
Silver Pebbles will also randomly appear near to a mine.