There's always the "brute force" method:

1. Take a layer with a known coordinate system that is supposed to overlay with your unknown layer.

2. Now make some educated guesses on what projection the unknown layer could be. (UTM, Plate Carree, etc). Project your known coordinate system layer into each projection until you find one that matches the unknown layer as much as possible.

Good Luck

There's always the "brute force" method:

1. Take a layer with a known coordinate system that is supposed to overlay with your unknown layer.

2. Now make some educated guesses on what projection the unknown layer could be. (UTM, Plate Carree, etc). Project your known coordinate system layer into each projection until you find one that matches the unknown layer as much as possible.