Both comportment and deportment denote conduct, demeanor, and behavior.
Deportment, however, seems to be reserved for a specific aspect of conduct, demeanor, and behavior, and that is physical bearing. In other words, deportment denotes how you hold or carry yourself.
We associate a stiff and dignified deportment with soldiers at attention before their superior officers, for example ("Ten-hut!").
Similarly, we associate relatively stiff and dignified deportment of people at special and particularly serious and somber occasions, such as swearing-in ceremonies, inaugurations, funerals, graduations, military parades, even job interviews.
On the other hand, comportment is the more general or generic of the two terms, and while the term is not without an element of bearing, that bearing is a reflection of good manners and effective interpersonal skills. Those skills could involve, for example, observing the appropriate amount of physical distance between yourself and others, what we often call "personal space."
A person with good comportment would neither get too close nor remain at a distance, depending, of course, on what propriety says is "just the right distance."
Here is where there might be overlap in the two terms. If propriety demands that good comportment requires a respectful distance between people, more than the distance between two close friends, for example, then the deportment of the person who is demonstrating good comportment would carry himself a little stiffly, with a respectful bearing.
"The fourth-grader's teacher gave him high marks for comportment. He was a well-mannered child who played well with others."
"The little girl's stiff deportment while in the presence of the headmaster changed quickly once she rejoined her classmates."
"The new employee made a point of having excellent comportment, especially when her immediate supervisor was in the room."
"At the Medal of Honor ceremony, the decorated Marine's deportment was exemplary, despite his need of a crutch to ambulate."