Discussion Forum—A Way with Words, a fun radio show and podcast about language

I have spent too much time arguing with my friends about what irony is and I need some clear and definite answers from people who know what they're talking about.

Here in my main question:

Can the word irony be used to describe the incongruity in a coincidence?

This is how it is most often used by people, but I have been told by others that a coincidence can not be ironic because there has to be intent involved. For example a sarcastic comment is ironic because of the incongruity of the of what the person says and what the person means.