I'm going to spill the beans about my cousin's marriage
Why would you want to reveal their secret?
I'm tired of hearing my family's praises for his wife. It is no good for the whole family.
There is nothing wrong with them praising his wife. It is not your place to reveal them being married yet, leave that to their discretion.
They need to tell the family now.
It is not your place to tell the family. It is your cousin's decision when the family is told. It is rude to want to do it for them.