Some people mentioned already a morality system, but instead, I think it should be way more harsh. After all, in the books and the movies, that spell isn't used all the time for a pretty good reason.

Quoting the wiki:

The act of committing murder, which was said by some to be an act of supreme evil, caused the murderer's soul to become damaged. However it had to be an act genuine and remorseless murder; a mercy kill or killing for self defence would not damage the soul.

When Dumbledore met Voldemort, after he started his crimes but before going to the Potter's house, he said his appearance was barely human at this point, as a result of having his soul split by Avada Kedavra, and having soul fragments removed from his body.

With they being said, I think using Avada Kedavra should cause an unremovable (and stackable) debuff. With every kill (which would have exceptions, considering the description from the wiki), since the soul of the caster is being damaged, the player maximum health and spell damage would be reduced, which essentially would make the player fell less inclined to use it, unless they were facing a REALLY strong opponent, or an opponent that was willing to kill the player instead of capturing/incapacitating.

There could also be a visual representation of such debuffs, changing the appearance of the player without necessarily having a morality system (I mean, I would like a morality system, but it isn't necessary for that to work).

EDIT: Since multiple people are getting confused with one of my points, I will clarify: yes, Voldemort was heavily deformed by creating horcruxes, which is why I mentioned soul fragments being removed from his body. Still, since we never see another person in the series using the killing curse as much as Voldemort (as per the Wiki, Voldemort was the character who used Avada Kedavra specifically the most), it's possible that damaging your soul actually causes some harm to your body, even if it's not as gruesome or fast as what happened to Voldemort.