I would like some suggestions on any type of evergreen that can be planted in pots getting morning sun only.

I would suggest Taxus (Yews) as a good evergreen for a shady location. There are both upright and columnar, and spreading varieties available. You could also use Emerald cedar, although the growth may become a bit looser depending on just how much light there is available. Make sure, however, that the container is large enough so that the soil doesn't freeze completely during a cold winter. For an evergreen I'd recommend an oak barrel (half wine barrel) size as a minimum.