I have no brother and sister but four cousins

没有错误，but有“除——以外”的意思，所以这句话意思是：我除了四个表兄弟姐妹以外没有亲兄弟姐妹。

可以否定提前
I don't have any brother and sister but four cousins.

I have no brothers and sisters but four cousins.
要复数啊

and 改为 or

and在否定句中应该变为or

有错误
正确的应该是：
I have no brothers or sisters but four cousins
no是否定词 后面不能用and 要用or
no=not any 后面要跟复数