I think this would be fairly easy. I think the best PoD is the Assassination Attempt of Napoleon III by Felice Orsini.
I would change it so the Emperor and Empress are wounded, but not killed. Historically they got out fine, and Napoleon III responded to an Italian Nationalist trying to kill him by completely supporting the cause of Italian Nationalism. If instead the event is suitably traumatic or damaging, it could cause him to develop a hatred, or at least wariness and dislike, of the idea.
Personally, I like this idea because it could, if you play your cards right, be a springboard for a Friendship between Napoleon III and Franz Joseph. They can bond over having both been the targets of Radical Nationalist Assassination Attempts.
At that point, you need Sardinia-Piedmont to embark on another ill-advised war against Austria. Difficult, as Cavour is pragmatic and understands the country's limitations, but not impossible as they made that mistake in 1848. Actually, here's where Not Killing Garibaldi (yet) could be very useful, as I could see him leading an initially successful rebellion in Lombardia, which draws in Sardinia, but then the rebellion and the Sardinian Armies are crushed by Austria.
Thus Austria has been the target of two wars where Sardinia-Piedmont sought to take territory from them with the backing of Revolutionaries, which is three too many. Now that France is also actively hostile to the cause, I could see S-P being divided up into Sardinia and Piedmont, with the Savoy dynasty effectively 'exiled' to Sardinia.
This further divides the north, ensuring that any southern revolution from mismanagement in Sicily has no support, which can drive a nice wedge between the North and South Italians. If the southern revolution goes badly enough you could see the Kingdom of Two Sicilies fall apart entirely.
Thus you've got everything you need for the Italian culture to start dividing into pieces, plus you've ensured that no one state is powerful enough to unite Italy by Force and the only country that was willing to help is now one of the powers actively keeping the peninsula divided.
Also, with Austria stronger and France friendly to Austria, this might butterfly German Unification as well.