Both sound wrong. ‘One’ doesn’t pair with ‘some news’ and should be omitted. (Which would you like to hear first?) Alternately, you could say ‘I have an item of good news and an item of bad news. Which one would you like to hear first?’ But even here, I’d probably skip the ‘one’, but it doesn’t sound wrong to use it.

1 is correct. 2 is wrong grammar.

I have some good news and some bad news. What do you want to hear first?

2

1