How to fade away loyalty to foreign countries?

[Sidney]

So, I conquered Naples as Sicily. Despite taking it from Naples, game says the province is loyal to Papal states now (probably because they have same culture and are alive?). My issue is that whatever I try, Papal loyalty keeps at 100 %, despite my cleric is on bolster culture mission whole time and I improved his skills regarding culture power. What can I do? I had dozens of rebellions spawning there and despite crushing all of them, loyalty remains at full. At least this should be changed, killing rebellion should change loyalty, it makes sense that killing population of other culture increases share of my symphatizers, right?

[DNLH]

You need to bolster your own culture power, Cathedrals, governors skills, right Goods, all that jazz. As Genoa I had my whole domain flooded with Papal influence and I only overcame it eventually after getting my Cleric to become the Pope and grant me the boosts from that, living in Pope's neighbourhood is a difficulty boost on its own, it seems.