I would say that the main tone of this poem is ironic or exaggerated. I believe that it is meant to be something of a spoof of traditional romantic poetry -- especially of pastoral poetry.
Traditionally, this type of poem would have the speaker telling his beloved that she should fall in love with him and they would be able to live happily ever after, generally in a rural setting (rural settings were seen as more calm and contented than urban ones).
In this poem, Marlowe still does this, but he takes it to a ridiculous extreme. He promises all sorts of things that could never possibly happen. Because of this, I think the best way to describe the tone is "ironic" or "exaggerated."