The weather forecast doesn't look very promising that day.
この場合、次のような言い方ができますよ。
ーThe weather doesn't look good on that day.
「その日は天気が良くなさそうだ」
ーThe weather forecast doesn't look very promising that day.
「天気予報はその日あまり良くなりそうでない」
promising で「天気が良くなりそうな」
ご参考まで！
It seems like the weather is going to be bad that day.
ご質問ありがとうございます。
・「It seems like the weather is going to be bad that day.」
（意味) その日はお天気が悪そうだ
<例文>It seems like the weather is going to be bad that day. Shall we reschedule?
<訳>その日はお天気が悪そうだ。日程変更する？
参考になれば幸いです。
カナダ 
アメリカ合衆国 
