今天晚上我可以不看電視。 in this sentence , 可以不 cant be use as a words, they are apart .今天晚上我可以不看電視。 mean you can choice watch TV , 今天晚上我不可以看電視 ,mean you cant watch TV, and the decision is not you cant change,
add.
when "可以不" is put on the end,mean it is Question
"可以不" can I ? is asking for the answer
"不可以" mean you can't
A:晚上我看下电视,可以不?
B:不可以。