Since he has to study and can't take time off to enjoy himself, I need to enjoy myself for his sake.
I want to also enjoy the time that he cannot have.
ご質問ありがとうございます。
なかなか日本語のニュアンスをそのまま訳すのが難しいのですが、原文に出来るだけ近いと思う訳にしました。
① "Since he has to study and can't take time off to enjoy himself,"＝「彼は勉強のため遊ぶ時間が無いので」
"I need to enjoy myself for his sake."＝「私は彼のため遊ぶ必要がある。」
② "I want to also enjoy the time that he cannot have."＝「私は彼が楽しめない時間を楽しみたい。」
ご参考までに。
He can't have fun because he has to study, so I'll have fun in his place.
この場合、次のような言い方ができますよ。
ーHe can't have fun because he has to study, so I'll have fun in his place.
「彼は勉強しなきゃいけなくて遊べないから、彼の代わりに私が遊ぶよ」
to have fun in his place で「彼の代わりに楽しむ」という意味です。
ご参考まで！
アメリカ合衆国 
カナダ 
