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Instead of ordering diplomatic actions by simply clicking in a province and using the bottom left menu go to the diplomatic screen where you can see relations to all countries. There you can change the envoy just before you take an action on the country by using the button next to the envoy's picture. Nonetheless the game always sends your best available character to a mission so you won't have a higher than 4 charisma character I'm afraid. Having a real job (any other than aedile, tribune of the soldiers etc) or being a faction leader in republics prevents a character being a diplomatic envoy if you want a better one make sure next time you reshuffle jobs you leave a high charisma character available for diplomacy.
It should also be mentioned that the game chooses high Charisma characters by default, which is good for diplomatic actions. If you're trying to assassinate someone, you want a character with high Finesse instead.