- I couldn't attend the meeting yesterday because there had been a death in my cousin's family.
- I can't attend the meeting today because there has been a death in my cousin's family.
In Number 2, has been is correct if the death was recent. This is because the present perfect connects the past and present. Basically the death is considered still recent enough to impact the present.
For this reason, you can still use the present perfect in Number 1, if you want to emphasize the connection with the recent past (yesterday) with the present.
In Number 1, had been is correct if the missed meeting occurred not yesterday but more remotely in the past:
I couldn't attend the meeting six months ago because there had been a death in my family.
In this case the past perfect indicates that the death occurred before the meeting.
You can also use there was in either your Sentence 1 or 2, but the subtlety of the perfect tense is absent.
Note: in American culture, most public and private companies allow 3 days off work for *grief* leave. But only if the deceased was a member of your immediate family, namely, a parent, spouse, or child.
If grandma or your close cousin or someone in your cousin's family dies, you won't qualify for grief leave.
So you may or may not get paid for missing that meeting simply because someone in your cousin's family died.