Blank Verse
Blank verse is great—no rhyming, no pressure. Just keep each line down to ten syllables. (Did you see what we did there? That last sentence was ten syllables.) "What a scam!" you cry. "Where was the rhyming, Shel Silverstein-style poetry I was promised as a small child?" Well, this is where the sidewalk ends... Shakespeare used blank verse. That's right—the bard. So your objections are futile, as is your resistance.
There is just one more catch to writing blank verse, though. Those ten syllables have to be in iambic pentameter. In "Frost at Midnight," Coleridge uses this meter to make his poem seem more like something you would really say. People don't typically talk in rhyming couplets, but non-rhyming iambic pentameter might actually get pretty close to the rhythms of real speech, sometimes. That's part of the reason Shakespeare used it—and if it's good enough for Shakespeare, it's got to be good enough for anybody, Coleridge included. In the twentieth century, certain Robert Frost poems like "Birches" and "Directive" use iambic pentameter to create the same vibe.
Oh, but what is iambic pentameter? Iambic pentameter is the meter for English language poetry: ten syllables of five unstressed and five stressed beats (each unstressed and stressed beat equals one "foot"). So the syllables have a rhythm like this: daDUM daDUM daDUM daDUM daDUM. If you happen to play the drums or know the basics about drums, that's kind of like lightly tapping a cymbal and then kicking the bass drum, and repeating that pattern five times.
You want an example? Here's one (more or less at random):
But thou, my babe! shalt wander like a breeze
By lakes and sandy shores, beneath the crags
Of ancient mountain, and beneath the clouds,
Which image in their bulk both lakes and shores. (52-59)
Check it: there are ten syllables in each of those lines and not a rhyme to be found. Plus, you can feel the rhythm pretty easily (daDUM daDUM…), just like a familiar or comforting convo with a good friend (or, you know, wise poet).