Have to smile at this question... it's hard to dig in a container so technically container gardening is naturally no dig I guess!
You can't do the normal layers of a no dig garden in a container because as they rot down the soil level will drop and you'll end up with a half filled container. So the only use for newspaper would be on the top to stop any weeds coming through if you've used garden soil and compost. You can then put mulch on top of the newspaper to conserve water and keep the temperature more even.
A container garden is a different kettle of fish than an open garden, so it's best to used a good potting mix that has some porous material in for good drainage.