How can I make pierogi gluten-free?
The main source of gluten in pierogi (the plural is pierogi, the singular is actually pierog) is the flour in the dough. You should be able to substitute regular flour for a gluten free version (eg rice flour) to make them gluten free. The same goes for whatever filling you are using, if you would regularly use flour as a thickening agent try corn starch or a gluten free flour instead. It's important to remember, however, that many gluten free flours do not bind as easily as wheat flour, and thus you may need to use more butter than usual.

EDIT

Pierogi dough, when made from scratch, dries very quickly, even moreso with gluten free flour. Be sure to cover the unused dough with a bowl and only take small chunks out at a time while you are forming and filling your pierogi.

Source: Was taught to make pierogi by an elderly Polish woman in my youth, have a niece and sister with celiac's disease