I wouldn't mind a cup of coffee right now.

I wouldn't mind.
私は気にしません［構いません］よ。
～が欲しい。／～を頂きたい。丁寧

I wouldn't mind a cup of coffee right now.
今すぐコーヒーを飲みたい。

I wouldn't mind a cup of tea.
《食事の誘いを断った後に》お茶を一杯だけなら。

I wouldn't mind a drink.
一杯やるのも悪くないね。

I wouldn't mind hearing what he has to say.
彼の言いたいことを聞いてもいい。