Poor irony, it's losing its meaning because even people who understand it find it hard to articulate what it is. What passes for irony is often Murphy's Law in action: If the worst can happen it will. And other interpretations. (A good site is Is It Ironic? where you can vote on whether a situation is ironic or not.)
Dictionary definition: Incongruity between what might be expected and what actually occurs.
Simpler: When what happens isn't in keeping with what's expected to happen.
So, for story purposes, a hyperactive librarian, a direction-challenged taxi driver, an ex-line backer child-care provider, a vegetarian werewolf, are all ironic combinations. The two are not just unexpected, but one half would seem to prevent it from coming together with the other.
A dramatic expansion on the definition might be: Irony is when a character's effort to avoid a situation then causes that situation to happen.
I don't know if the "effort to move away then leading to" is necessary for something to be ironic, but it creates tension and conflict which are always good for stories!
Another, harder to picture at first, but more obvious when you get it: When mutually inclusive factors bring mutually exclusive factors together.
The bullied would avoid the bully but what if the bullied became principal and the bully became a father of -- to add further irony -- the valedictorian? The tow truck that shows up to pull the car full of Young Republicans out of the ditch is driven by a gay black woman.
For the following character types (including the 4 listed in the first paragraph), set up situations such that the character's choices (a one time choice or a lifetime of choices) creates the expectation that something won't happen, but then a choice of theirs causes that thing to happen.
To add extra irony, choose personality flaws and values that are the opposite of what's expected. Check Chaotic Shiny's Motive generator and Death Quaker's Big List of Merits and Flaws for ideas if you need them.
What situation would make this person feel like a fish out of water?
What skills and beliefs of the character would be challenged by the new situation?
What choices might such a character normally make -- like getting married, job searching, going to religious services, having a child -- that might, ironically, cause them to end up in this situation?
What could the character want that might unexpectedly connect to this situation, thus forcing the character to deal with it?
A couple more common forms of irony used in stories:
Verbal irony: Saying the opposite of what's meant. If the intent is to disparage someone, then it's sarcasm.
Dramatic irony: When a character expects the situation to be one way, but the reader knows more and is aware the character's expectations won't be met.