The speech is ironic because Scrooge accuses the ghost of being indigestion rather than admitting he is afraid of him.
The ghost asks Scrooge why he doesn't believe in him.
A slight disorder of the stomach makes them cheats. You may be an undigested bit of beef, a blot of mustard, a crumb of cheese, a fragment of an underdone potato. There's more of gravy than of grave about you, whatever you are!” (Stave One)
Irony is when you say the opposite of what you mean or when the opposite of what you expect happens. There are three types of irony. Verbal (the first kind), dramatic (when the audience knows something the characters don't), and situational (when the opposite of what you expect happens).
You would not expect a person to argue with a ghost. Most people are afraid of ghosts. It's the natural reaction! When Scrooge's old partner shows up, he is naturally surprised. He expresses his shock with resentment and denial.
The ghost convinces Scrooge that he is there for his betterment, and he is trying to help him. Marley, Scrooge's old partner, wants to help Scrooge avoid the mistakes that he made as a living man.
In the end, Scrooge grudgingly agreed. After all, he will have to believe in and listen to three more ghosts. Ironically, he will confine to argue and it is this arguing that will contribute most to his personal growth. That's irony because it's the opposite of what you'd expect. A grumpy Scrooge will learn more here than a compliant Scrooge, because he is essentially getting the sense knocked into him by this whole event!
The moral of the story is that Scrooge went from being a grumpy old miser to a caring man in one night! He would not have been able to do this without Jacob, the ghost!