Coyle's sunglasses act as a parody of Lady Justice's blindfold
Lady Justice's blindfold symbolizes impartiality and objectivity in the legal system. She herself is the allegorical personification of law, embodying the idea law should be applied without prejudice. Coyle similarly claims to be the law (his stunned voice line), equating himself to the role of Lady Justice.
His sunglasses function as an obstruction to his eyes much like Lady Justice's blindfold. However unlike Lady Justice, his 'blindfold' obscures his eyes only from the viewer while leaving his own vision unhindered. It projects the illusion of impartiality to onlookers while allowing him to act upon his own prejudices.
This reflects the very institutions his character critiques while enforcing the core of his character as a corrupt cop. He, as a law enforcer, should blind himself to personal bias. Instead, he perpetuates a false justice driven by prejudice.
