I don't know what you mean by limited sun, but if you had some success with parsley you also should have good results with chives, sage, basil, dill, oregano, and cilantro. I would use a pot with a diameter of a five gallon bucket. Self watering containers would do fine .
You might like to try a 'pick and return' thing like leaf lettuce. Not a herb, but why not try it?
Also, a patio tomato in pot or any tomato in hanging planter could be fine as well.
You can get instructions on making self watering containers and hanging tomato planters on YouTube.