I searched Google for methods of cleaning room humidifiers, cause I think e-cigs pretty much work the same way, and found people recommending white vinegar. I think Frankie recommended boiling in vinegar. Only with the humidifiers, no one mentioned boiling, just vigorous shaking.
I think the whole boiling thing might work slightly only because the water or whatever other liquid you're using gets agitated by the bubbles. The heat may help as well, but I think agitation is key here, along with vinegar.
My M401 atomizer performance was falling off recently. I wanted to just drop it in a bottle with some vinegar and shake, but the M401 atomizer has vital parts exposed and I didn't want it knocking against the sides of the bottle during vigorous shaking, lest it get damaged.
I concocted a little contraption you can see in the attached photos. It's a slightly modified bottle cap. The M401 atomizer fits right in the top, I put my finger over it, then shake vigorously. The atomizer stays stationary while the vinegar swishes all around it. It seems to have worked nicely. With a flashlight I can see that all the black gunk is gone from the actual heating coil, and it's performing a lot better.
For a pen-style atomizer, nothing is exposed cause of the tube they're attached to, so when I need to clean that I may just drop it in a bottle and shake.
PS. I shake with plain water after all that, to rinse off any remaining vinegar before vaping.