Relativistic Space Travel Question

A question for you physicsy folks out there (astrogirl?). I'm writing a story that hinges on time dilation in space travel, and to get the sort of time dilation I need for the story to work, I need to reach speeds around 0.9c or higher.

My question is what kind of drive could I posit these people are using? This story is not set in the super distant future: a few to several hundred years. And I can trade on the idea that a lot can happen in 100 years of unexpected innovation (as we've seen in the past), but they're not gods or anything.

These ships are not multi-generational. They are designed to get people from point A to point B in not more than a few years, ship time. (In terms of living space, they are closer to Andy Weir's Project Hail Mary than KS Robinson's Aurora. I'm thinking they rely on acceleration for simulated gravity, not rotation.

This society does have access to lots of raw materials, ranging from bodies to mine to stars, nebulae, etc., and they have big, fast 3D printers.

I want to reasonably appease an audience that is not picky about very hard SF but would like some semblance of scientific plausibility.

Thanks!