documentclass{report}
usepackage[tocgraduated]{tocstyle}
usetocstyle{standard}
begin{document}
tableofcontents
chapter{duck}
chapter{goose}
chapter{hen}
chapter{hen}
appendix
renewcommand{thechapter}{Roman{chapter}}
%renewcommand{thesection}{Roman{section}}%If there are no chapters
chapter{duckling}
chapter{gosling}
chapter{chick}
chapter{poult}
end{document}

usepackage{etoolbox}
makeatletter
patchcmd{appendix}{@Alph}{@Roman}{}{}
makeatother