Thank you Rohit and Henrik, Rohit's solution does pretty much what I want. When I use Henrik's solution I get no Frame. This works:

ListLinePlot[shortCoordinates[[n]], ImageSize -> {128, 128}, 
  Frame -> False, Axes -> False, AspectRatio -> 1, 
  PlotMarkers -> {{\[FilledCircle], 2}} ] // Framed, 

All did was add the // Framed recommended by Rohit and it worked perfectly.

If I use Henrik's suggestion as in:

ListLinePlot[shortCoordinates[[n]], ImageSize -> {128, 128}, 
 FrameTicks -> None, Axes -> False, AspectRatio -> 1, 
 PlotMarkers -> {{\[FilledCircle], 2}} ] ,

I get my graphs but with no frame.

Finally, if I use Henrik's solution with the addition of // Framed I get what I want, which is my graphs with a simple black square surrounding them.

Thank you both.

Now, If only I could figure out what most of the graphs use the whole range of [Xmin, Xmax] along the X axis and [Ymin,Ymax} on the Y axis BUT a few graphs (about 4%) use the [Xmin,Xmax] range on the X axis, but only part of the [Ymin,Ymax} on the Y axis where there is space below Ymin and above Ymax on the Y axis. Any clue?

For controlling ticks on a frame you should not use the option Ticks but FrameTicks, in your case:

FrameTicks -> None

Hi Henrick,

One way

coords = RandomReal[10, {10, 2}];

ListLinePlot[coords,
  ImageSize -> {128, 128},
  Frame -> False,
  Axes -> False,
  AspectRatio -> 1,
  PlotMarkers -> {{\[FilledCircle], 2}}] // Framed

Check the docs for Framed.