Here are a few corrections and suggestions for this translation:
"Blue eyes, you don't cry" does not reflect the original very well. "No llores" is a command, so it would be better translated as "Don't you cry" or "Don't cry". Same with the second line: "No llores ni te enamores." -> "Don't (you) cry or fall in love".
"Love me for the whole life" is too literal a translation and is not grammatical in English. "Quererme toda la vida" should be translated with a possessive pronoun rather than with an article. It could be interpreted as "Love me for my whole life" or "Love me for your whole life"
"Poison to kill me" is not wrong, but the reflexive "poison to kill myself" would be better; "poison to kill me" would normally be used when the killer and the one being killed are different people.
I hope this helps! :)
Writer: Manuel Casazola Huancco
Versión de Violeta Parra
http://www.cancioneros.com/nc/1153/0/ojos-azules-manuel-casazola-huancco