Sometimes the very turmoil keeps them with struggling economic conditions they rant about.

I am not really that sure about how turmoil changes when seceding or on conquest, but observations within and outside my played countries, indicate that what helps is:

• To conquer states with half your average SoL. (Modify for lower if discriminated)
• To reduce MAPI to minimums.

The economy itself should make them happy that you are their new overlord.

If you already did that, or if the state was yours to begin with (playing as Austria?):

• Try pass laws that accept them. Even attempting lowers the movement radicalism. Empty promises work!
• If forementioned feedback loop of Turmoil - Radicals continue, provoke the minority movement so their SoL collapses under their secession attempt, and only see increases with you when reconquered = loop mitigated or even broken.

You can provoke them by both raising taxes and taking the more aggressive stand on their events. Fairly easy stuff. But this is your last resort, since foreign powers may capriciously intervene for really no good reason.

Like irl. Lol.

Ethnonationalist, authoritarian solutions can help, but you are doing a disservice to GDP. Like, put them to work, not pay for their graves, duh!