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I know we can negate place, manner, etc. by just placing a 不 before the verbs (prepositions) that introduce the clauses.
我不在中国工作。
他不坐车去工作。
But how can I negate time, since it doesn't have a verb/preposition before it?
For example: I wake up not at 8am, but at 9am.
Would I have to place a 在 before the time?
我不在8点起床，我(在?)9点起床。
Would this be the only mandatory 在 when we talk about time or are there other situations it's required?
Thank you for any help!
I am a bit confused by the 在 in your example sentence, since you don't need it there, 我不在8点起床，我(在?)9点起床。 Frankly, I wouldn't know what this sentence was supposed to mean, if you hadn't provided a translation. If you want to express that something occures at a certain time of the day, e.g. X o'clock, there is no need for 在, just use X点 or X点钟.
As for the proper way:
我不是8点起床，我9点起床。
不是 can be used for such cases, to negate a certain aspect and then to point out the correct aspect immediately afterwards. E.g.
我不是骑车上班，我坐出租车上班。 I do not ride the bicyle to work, I take a taxi.
EDIT: I can still recall the first time I had learned this 不是 structure and I was confused by it since it sounded odd to me. To get an idea of the difference between 我8点不起床。 and 我不是8点起床。, you have to understand that the first sentence simplay negates the whole statment, while the latter sentence negates only the aspect that is immediately after 不是.
The given translation in this answer is an example of the "是...的" pattern for emphasizing a particular aspect of a phrase. It is not specific to time; for instance:
我不是跟朋友吃晚饭的，我是跟爸爸妈妈吃晚饭的.
I didn't eat with my friends, I ate with my parents.
You may certainly use 在 to reference time, and you can negate it thus:
不是在八点起来，而在九点才起来。
You do need to use 是 though, otherwise 不在 will take on the meaning of existence or location.
However, using 没 is more common: 八点还没起来，而九点才起来。
In both cases you are not negating time itself, but the action taking place at a certain time.
This is logical, in any language, even in your example, as you just make a trick with word order. Your "not" still references your action of waking up, not the time itself.
Search, and you will find instances of 不在 + time: 为什么世界杯不在八点放？
In my mind, this is rather ungrammatical, though, or a short form of 不是在.
