"He always gives an outward appearance of being cheerful when he's out in public."
"He always acts cheerful on the outside when in public."
"He always gives an outward appearance of being cheerful when he's out in public."
"He always" 「彼はいつも」
"gives an outward appearance" 「表面上振る舞ってる」
"of being cheerful" 「明るく」
"when he's out in public" 「人前に出ると
"He always acts cheerful on the outside when in public."
"acts cheerful" 「明るく振る舞ってる」
"on the outside”「表面上だけ」"on the surface" も言えます。
"when in public" 「人前に出ると」
I try to look cheerful in my outward appearance whenever I'm with other people.
I always try my best to project an air of lightheartedness in the presence of others.
この場合、次のような言い方ができますよ。
ーI try to look cheerful in my outward appearance whenever I'm with other people.
「人といるときは、うわべは陽気に見せている」
to try to look cheerful in one's outward appearance で「うわべ・外見は陽気に見せる」
ーI always try my best to project an air of lightheartedness in the presence of others.
「人前ではいつも陽気な雰囲気を出すようにする」
to project an air of lightheartedness で「陽気雰囲気を見せる・示す」
ご参考まで！
オーストラリア 
カナダ 
