Echoing a bit, and adding to, what some others have alluded to here:
1) have another, higher offer in hand. As others have said, make sure you are willing to move to the other position before taking this approach. If you have an offer in hand, but are not willing to take it (why did you apply if this is the case - perhaps this is a whole other post), I wouldn't try to leverage a raise. If they say, "no raise", and you stay, in such a case, they very well may not take you seriously if you have another offer in hand in the future and try this approach.
2) Do something spectacular, relatively speaking (i.e., how this is defined might depend upon where you are at and what expectations are like in your specific area). Even under these circumstances, it is potentially helpful to demonstrate a pattern of "good things" happening, as opposed to having one thing "spectacular" happen. This is hard to define, and may vary across institutions and areas.
As an example, I had a paper published in one of the top journals in the field, and my chair decided to put me forward as a candidate for an "off-cycle" raise. We sat down together and crafted a short letter illustrating the publication, but also pointing to high productivity in peer-reviewed journals, that such productivity was complemented by high citation rates for some of the papers (some of the highest in my department in a few of the years), pointed to a funded grant and a pattern of fairly competitive grant submissions that didn't end up being funded, and that I was providing excellent mentorship to undergraduate students (illustrated by including a spontaneous email from a former student now in graduate school) and to graduate students.
Subsequently, I was asked to interview for another position (I didn't end up with an offer). However, before the interview, I let my chair know that was going on the interview, and my chair used it as a reason to nudge the dean on the "off-cycle" raise. Things moved quickly after this happened, and the provost wound up adding to the figure the dean had approved and passed on.
Long story short - have a compelling reason for asking for a raise, and one that can potentially be backed by "numbers" that are easy for people to understand. A reason that basically equates to "I've been doing my job, and haven't had a raise in a while" is probably insufficient.
Hope this helps!