The RadButtons suite uses VisualStates to change its appearance in the different control's states (check, normal, clicked, hovered, disabled, etc.). Those visual states are located in the ControlTemplate of the button and they cannot be modified easily.
As Peter mentioned, in order to modify the checked color to green you can extract the ControlTemplate of the button and modify the visual element that represents its checked background.
I attached a sample solution that demonstrates and approach with modified template and an attached property.
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