The relevant page of the Irish government is Family Members of EU/EEA/Swiss citizens:
Family members of EU/EEA/Swiss citizens seeking to reply on Directive 2004/38/EC (Free Movement Directive) – type of visa for which you should apply
If you are a non-EEA national:
- who does not hold a document called “Residence card of a family member of a Union citizen” as referred to in Articles 5(2) and 10(1) of Directive 2004/38/EC on the rights of citizens of the Union and their family members to move and reside freely within the territory of Member States, and
- wishes to accompany or join an EU/EEA/Swiss citizen family member who is moving to or residing in Ireland pursuant to the Directive 2004/38/EC,
You can apply for a single journey short-stay C visa which will permit you to enter and reside in the State for up to 3 months.
Later, it notes that the spouse of an EU/EEA/Swiss citizen is among those "qualifying family members" who are exempt from the visa fee.
Now you may be concerned that the text says "moving to or residing in Ireland," but it also says "pursuant to the Directive 2004/38/EC," and if you look at the directive, it is clear that it applies to short visits. I have come to the conclusion that "move to" is a mistranslation, because in other languages the verb used in that position can also be translated as "travel to" and, more importantly, lacks any sort of connotation of a long-term change of residence. I haven't found any court cases that clarify this, however.
The Irish page also notes that you will need "proof that [you] are exercising free movement rights in Ireland [for example] ... a declaration or statement of confirmation." Your wife's visa application should therefore state explicitly that you will be traveling with her to Ireland.
The instructions further note that the visa in this case will be a single-entry visa, which is troubling because it suggests that Ireland does not share my interpretation of the directive as applying to short-term travel. If you run into trouble with that, you might consider bringing it to the attention of SOLVIT.