Translation:Sorry, we don't have time.
No, it's pretty good. We're not available, We're not free, We're busy, We don't have time. (All have about the same meaning)
Is 对不起我们没有时间 really incorrect? I say this all the time, and no one has ever corrected me.
I was curious as to how to make this sentence past tense given that it contains "沒" already. Apparently, one has to use "以前" ("before"): "我們以前沒有空。"; "我沒沒有空。" and "我沒沒有有空。" are apparently nonsensical.
Exactly! However, I do not think that "past tense" is an independent grammar in Chinese. Maybe "我们以前没有空" sounds a little weird to me just as "We were not available" does.
To express the meaning of "before", I believe that you can use "以前", "从前", "之前" or just a single "前". Though in Chinese, the four words sometimes have subtle differences which can even make Chinese native speakers confused. Hope these examples would make some sense:
很久以前，一位王子爱上了一位公主 <-> A prince fell in love with a princess long ago.
从前，一位王子爱上了一位公主 <-> Once upon a time, a prince fell in love with a princess.
在第一次世界大战之前，一位王子爱上了一位公主 <-> Before the World War I, a prince fell in love with a princess.
一百年前，一位王子爱上了一位公主 <-> A prince fell in love with a princess 100 years ago.
“We were not available" is perfectly fine in English. The past tense in Chinese is often implied, which can be a bit difficult when you want to speak very precisely and that's just not how it's done.