"Mike was a bad drunk. Brett was a good drunk. Bill was a good drunk. Cohn was never drunk." (SAR 153).Based on recent class discussion it is apparent that Cohn doesn't have the same sense of ironical humor as all the other characters. He gets offended easily at things that are meant to be jokes and never makes any jokes himself. He is a very straight and literal person, and that personality doesn't seem to fit with everyone else's carefree attitude. He isn't able to see underneath someone else's comment to see the ironic joke that everyone else gets. This lack of irony estranges him from the rest of the group. They just don't like him. It's hard to say if getting Cohn drunk would actually solve this problem and give him a sense of irony, since some people are bad drunks, but maybe getting drunk would help him to relax and see the comedy in the jokes that everyone else make.
The direct opposite of Cohn, I think is Bill. He is probably the closest we have to someone that is an actual alcoholic in the book, but he is also the one with the largest sense of humor. Bill is the epitome of irony, everything he says has to be ironic. "Irony and pity" is his motto, and the pity part is likely ironic too. But more often than not he is completely wasted. Take his trip to Vienna for example. He doesn't remember anything about it, except for one story that is probably only loosely true, but hilarious nonetheless.
Before Mike had his outburst at Cohn, the group of friends gathered together to drink and talk. The alcohol helped them to feel more relaxed and enjoy each other more. The irony is the culture that they are a part of and the style in which they find their humor. I think that getting at least a little tipsy might be conducive to ironic humor the way it is portrayed in The Sun Also Rises.