1
I want to tell you a very good news.
I want to tell you some very good news.
I want to tell you a very good piece of news.
News is an uncountable noun, so do not use a/an directly before it.
Use some news or a piece of news: ‘I’ve got some good news.’ ‘I’ve just heard an interesting piece of news.’
2
The news on TV are always sad.
The news on TV is always sad.
Although news ends in -s, it is singular and takes a singular verb: ‘The news is good.’ ‘This news was unexpected.’