When could this happen?
Well, technically you could have a Muslim majority Italy. Wasn't Iberia 80% Muslim at one point?I don't think you can ever actually get a Muslim Majority Italy, however Italy under Islamic authority is doable in the same way that parts of Iberia were.
That said, sometime between the late 15th century to early 17th century would be the petriod it's possible for Mainland Italy.
However, if we include ALL of Italy, this did happen IOTL, with the Emirate of Sicily (965-1072).
Wasn't Iberia 80% Muslim at one point?