In the incident with Tim Johnson, Atticus shows courage by stepping out into the street in front of a rabid dog that could attack him at any moment. However, the more courageous thing is that Atticus has not boasted of his ability to shoot. It would win him points with both members of the town and with his own children, who view him as "feeble", but he is not willing to do so. Atticus does not believe that having the ability to shoot makes him a better man - in fact, he doesn't like having the skill - and so he is brave enough to show discretion instead of try to "get something" ouf of the skill.
In the case of Mrs. Dubose, the courage comes in her ability to challenge an addiction. Not only does she challenge the addiction to morphine, but she does so knowing that she will soon die - so, in essence, it doesn't matter if she is addicted or not. However, Mrs. Dubose does not want to die an addict; it is more important to her that she beat the addiction and die a free woman.