Short-coated

The OED (229) and Collins (75) associate short coating with infant attire. Chambers (72), on the other hand, notes that gondoliers wear short coats; so the expression may refer to their becoming gondoliers. That seems a more likely interpretation, given that in their next line they refer to being devoted to [feminine] beauty.

Context: 
Since we were short-coated
Act: 
Act I