Do I understand you correctly that you want to force convert the country and take their capital in the same peace deal? Then the old capital(which now belongs to you) will be converted and if it has a CoR it will be removed. But their new capital will not be converted and a CoR in the new capital will stay. To remove a CoR from the new capital, you need two peace deals. In the first peace deal, you take the old capital, but don't convert the country. And in the next war, you convert the country and this will convert their capital.
@wielkiciensteam are you claiming that force converting a country and taking their capital in the same peace deal will convert the province to which the capital moves? (and not the province in which the capital was before the peace deal). Or did you understand the question differently?