If you reduce the kinetic energy of molecules, bio processes eventually just stop completely. Given that “biological processes stopping completely” is usually take to be synonymous with “death”, you don’t want your field to be doing that under the hood. If you want to mess with time, mess with time, not biochemistry.
The most plausible scenario is, of course, relativity. I imagine a metric
$$\mathrm{d}s^2=c^2 \mathrm{d}\tau^2=\left(\frac{1-\tanh(\sigma(r-R))}{2k}\right)c^2 \mathrm{d}t^2-\mathrm{d} x^2-\mathrm{d} y^2-\mathrm{d} z^2$$
which produces a localized region (a sphere centered on the origin of the coordinate system with radius $R$ and boundary “tightness” $\sigma$) where time moves more slowly by a factor of $k$ (in the limit of large $\sigma$). I have not calculated the stress-energy tensor associated with this metric by the Einstein field equations, but I expect that when I check it later it will have very large values.
Unfortunately, this will never be portable. I have done a lot of research on low-energy gravity manipulation and I’ll just say that it’s hard to find a solution that doesn’t require asteroids or moons compressed into tiny boxes moving at near-lightspeed to work.
I can’t think of a better solution.
On the other hand, why are you trying to explain this?
A very common question on this site is “I have this really cool device, how do I explain how it works?” and my answer is often “don’t try” (if in comments, not answers). You do not need to explain absolutely everything in your stories scientifically; I as a reader am often quite bored when the author tries (and inevitably fails). If this device is important to your plot, and you can’t think of a decent explanation, and if having an explanation isn’t equally critical to the plot, then just handwave it.
Often works like Interstellar are praised for being scientifically accurate and successful at the same time, but simultaneously Star Trek is sometimes considered one of the top sci fi franchises of all time and isn’t even sort of scientifically-based. Handwaving is okay is what that teaches us.