Java diamond-shape isometric map tile pick

First register a MouseListener to your panel (the panel where you want to draw your tiles). Now, according to your rendering code you actually "know" where each tile starts. So all you have to do is calculate which tile was clicked.

JPanel gamePanel = new JPanel();
gamePanel.addMouseListener(new MouseAdapter() {
    @Override
    public void mouseClicked(MouseEvent event) {
        int x=event.getX();
        int y=event.getY();
        System.out.println("clicked at ("+x+","+y+")");  //these co-ords are relative to the your gamePanel           
    }
});

EDIT:

I changed to code above, it wasn't correct. But I am sure you'll figure it out. So above code shows you how to add a MouseListener to your panel/frame. And if it works, you should be able to see in the console where you click.

Now you only have to calculate which tile was clicked:

(x,y) --> + - - - 
          '    /\
          '  /    \
          '/        \
           \        /
             \    /
               \/     + <-- (x+36, y+18)

your mouse pointer needs to be somewhere between the two points (x,y) and (x+36, y+18). Of course there is the additional problem that someone could click somewhere between (x,y) and (y+36, y+18) but still not click on the tile (maybe someone clicks on the tile top left of it) and there you may need to decide which tile you want to be selected.

Another way would be to divide your panel into a panel of squares. But without drawing them of course. Imagine that each tile could have a square in the middle:

               /\
             /____\
           / |    | \
           \ |____| /
             \    /
               \/    

something like that. so you only need to calculate if someone clicked inside the square.