I've found Contis in general to be a bit harder to seal and take up to a few weeks of riding before they settle down. I've tried Mountain King II and XKings both the "Protection" versions I also have friends who have tried this.
Two things that might help
1. Before fitting wipe the inside of the tyre with Isopropyl Alcohol. The theory is it removes the "release compound" which the sealant might have issues with.
2. Put lots of sealant in (like 150-200ml) and ride for a couple of weeks. You can then remove the excess sealant if they've settled down (either using a syringe through the valve or by pulling one side off the rim). Riding generally seems to be much better than wheels sitting in the shed for sealing.
I've fitted 3 new Mountain King 2s and an XKing and the last two I fitted seemed to be better using the techniques above. Obviously I've not done an "A/B" test so this is just my experience. My current fix is to buy Maxxis instead which seem to go up no problem.