Review the music you have already written and consider its mood. Is the song a happy, feel-good number? Is it a heartbreaking, melancholy piece? Your lyrics should reflect the mood created by the music. You can determine mood by the number of minor chords the song has (which usually indicates a melancholy tune) or the rhythm and tempo (if it's fast, you might want to consider upbeat lyrics).
Write what comes to your mind and try to employ a rhyme scheme. Rhyming songs are the most memorable, since they are the most singable. Remember that lines can rhyme internally and rather imperfectly ("Your love, your love, your love is my drug," etc.), or at the end of the lines to be effective.
Write your song with just one instrument in mind. Avoid thinking about songs that would sound amazing with a full band since you are composing an acoustic number. You will not have backup vocals, so write your lyrics based on a melody line that is easily singable for just one person. Many times, a "storytelling" approach works well for acoustic songs, where the song is more narrative. For instance, The Ataris "Looking Back On Today" works well acoustically because the singer is relaying moments from a specific relationship.
Record yourself practicing lines. Sometimes you might come up with a good idea that simply needs a bit more development. If you are recording your musical "brainstorming," you can easily recall and employ those ideas in your acoustic song. Additionally, if your song is inspired by another person, review notes or journal entries you have written that contain raw emotion and conversational verbiage. This type of writing will connect with a variety of listeners.