For example, テレビをみませ is "I will watch TV". I would like to say なにをテレビをみますか but I'm not sure the double を makes any sense, for example in なにをみますか the person may answer テレビ but I want to know what is on the TV that they watch?
EX2:
としょかんでほんをよみませ
I will read book/s in the library.
なにをほんをよみますか
What book/s will you read?
EDIT: Note that I am not looking for an adjective answer like good, scary, fantasy, but the specific name of the book/show.
First of all it should be テレビをみます. You did this twice, so I'm assuming it wasn't a typo.
You wrote:
なにをテレビをみますか
You're intuition is correct that you cannot use を twice. For this you use the particle で, which means 'on' in this context:
何{なに}をテレビで見{み}ますか。
Using を doesn't make sense because you are not watching the TV, you're watching a programme on TV. Using を with なに is correct because the answer to the 'what' question is the thing that will be watched.
In your second example you wrote:
なにをほんをよみますか
Both 'what' and 'book' are valid objects on their own ("What will you read?"/"Will you read a book?"), but not together. The sentence "What book will you read?" has a single object which is "what book". In this case you can say something like:
何{なん}の本{ほん}を読{よ}みますか。
Aside:
If you did want to ask "What kind of book will you read?" as in scary/fantasy etc., It would be:
どんな本を読みますか。
