This is a very broad question, because you would have to define discord. I suppose that the biggest discord is when Baba and Amir have to leave their beloved country and move to California. There is a discord of place, culture, social class, and pretty much anything else that is familiar.
Baba deals with discord by working hard and doing what needs to be done to keep the family in tact. However, he is still a proud man and desires to keep the old ways. For example, he gets angry at the owners of store, when they ask him for his ID as Baba wants to pay by check. In a word, he has a hard time fitting in. However, it should still be stated that Baba is a man of integrity, courage, and hard work. All of this comes out even in the context of discord.
Ali is a minor character of the novel. He is the acting father of Hasan. He is also the servant of Baba. He is relatively poor, as he is an ethnic Hazara. He also walks with a limp, which was caused by polio. When it comes to discord, he just accepts it humbly and deals with it without a fight.
Ali nearly always takes his problems in stride, always in the quiet, humble manner in which he lives. When older boys "mocked him when he hobbled by," Ali never says a word. When Hassan is born to his wife, Sanaubar (despite the fact that Ali is sterile), Ali pretends that the boy is his own son, and not Baba's--just as Baba must have requested. A man who is incapable of showing facial expression except through his eyes (due to the "paralysis of his lower facial muscles"), only twice does Ali show any real emotion in the novel: He becomes angry when he catches Hassan and Amir shooting walnuts at the neighbor's dog and using a mirror to reflect light into their neighbors' eyes. He
... get mad, or as mad as someone as gentle as Ali could ever get. He would wag his finger and wave us down from the tree... scowling at his son. (Chapter Two)
When Hassan is accused of theft--and then forgiven--by Baba, Ali decides they must leave the household. "They'd both been crying," and Ali
... glanced my way in his cold, unforgiving look...
His mouth twitched, and for a moment, I thought I saw a grimace... not even Ali's paralyzed face could mask his sorrow. (Chapter Nine)
Baba is far more emotional dealing with discord. Sometimes he "bellowed" when he needed to get his way. Other times he simply "heaved a sigh of impatience." At times, he retreats to the "smoking room," where he drinks his disgust with Amir away with whiskey and small talk with Rahim Khan. Usually, he does just as he wishes, most often with positive results. When he is told his plans to build an orphanage are impractical, Baba goes right ahead and proves his dissenters wrong. On his flight from Afghanistan, Baba threatens the Russian soldier at the risk of his own life, but the Russian--bent on raping one of the passengers--backs down. But when Baba relocates in California, he loses the power and confidence that always propelled him to greatness in Kabul, and he is forced to work long hours at a convenience store and sell second-hand goods at flea markets on weekends. Baba mellows in America, where he accepts his new position as a lower middle-class immigrant. And when he discovers he has cancer, he refuses treatment that may only prolong his life and accepts the fate that Allah has bestowed upon him.