The Caroleans did not carry any rank insignia on the uniform. However, there were several ways to distinguish an officer from a regular soldier on the uniform.

First of all, the lining and socks of officers and NCOs were usually blue while the colour of the regular men were determined by their regiment (most had yellow, but some had blue or red). This means the coat turnups, the coat arm turnups and the collar was blue instead of the regiment colour.

Captains and above were allowed, if they could afford it themselves, to add gold lacing to the coat turnups, coat arm turnups, collar and the pocket lids. They could also use gilded buttons.

Lieutenants were allosed to add silver lacing to the coat turnups, coat arm turnups, collar and pocket lids. They could also use silvered buttons (regular soldiers used tin buttons).

Officer's coat.

Private soldier's coat (this one is with yellow lining, the most common one).

Officers and NCOs also wore a metal collar in the shape of a crescent. It was their rank insignia when on duty.

Here you can see the various collars and how they were worn.

If you need any information on how Carloean soldiers were recruited, trained, fought, discplined, what food they got and so on during this era to make your story more realistic, give me a shout and I will be happy to help.