First of all, it should be "some news isn't." It's weird, and I never even noticed it before. I was about to say "'news' is a singular noun even though it ends in an 's,'" but I just checked a dictionary and it says it is "a plural noun (used with a singular verb)."
Now, we come to a difficult issue of semantics and culture. Up until fairly recently, it was understood that "news" by definition meant a kind of information--something accurate, correct, and true.
You could certainly say "Some news today isn't true." That is correct English and would be understood.
The word "today" is fine, I would probably make it vaguer by saying "these days."
But because of my age and background, I would add something to recognize that if it isn't true, it shouldn't be called "news."
"Some 'news' these days isn't true."
"These days, some so-called 'news' isn't true."
I might go farther in explaining where you need to be careful:
"Some 'news' these days, especially on the Internet, isn't true. Be careful!"