In the given line "I could stare into your eyes as / a thousand years come and go," the literary device used is a **hyperbole**.
1. **Hyperbole** is a figure of speech that involves extreme exaggeration to emphasize a point. In this case, the speaker exaggerates the idea of staring into someone's eyes for a thousand years, which is not meant to be taken literally but rather to convey intense emotion or depth of feeling.
2. The phrase "a thousand years" is not meant to be understood as a literal time frame but rather as a way to express the depth and eternity of the speaker's emotions or connection to the person they are addressing.
3. By using hyperbole in this context, the speaker conveys a strong sense of everlasting love, commitment, or intensity of feeling towards the person whose eyes they are looking into.
Therefore, the correct answer is **hyperbole** in this line.