Are painless rubbery chronic (2-3 years) enlarged lymph nodes in posterior triangle of the neck always cancerous?

Not likely. If the nodes have not changed in 2-3 years, it is unlikely that these are cancerous. More than likely it is due to something in your scalp that may be causing low grade chronic inflammation.
Need exam. The only way to get the answer you are looking for is to see a doctor and have an examination. It is not possible to answer your question in the forum. Call a doctor. Good luck.